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EdacT
^■570.
D
EXERCISES IN
MENTAL
ARITHMETIC
D
MIRICK- BALLOU-TALL
D
^:io.t.- T //9^20.^'PD
^arbari College iiftrarg
LIBRARY OF THE
DEPARTMENT OF EDUCATION
COLLECTION OF TEXT- BOOKS
CONTRIBUTED BY THE PUBLISHRI^S
TRANSFERRED
TO
HARVARD COLLEGE
LIBRARY
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3 2044 097 009 286
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PRACTICE EXERCISES IN
MENTAL ARITHMETIC
BY
GEORGE A. MIRICK
IN8TBUOTOB IN EDUCATION, HARVARD UNIVERSITY
FORMERLY ASSISTANT COMMISSIONER OF EDUCATION
STATE OF NEW JERSEY
FRANK W. BALLOU
SUPERINTENDENT OF PUBLIC SCHOOLS
DISTRICT OF COLUMBIA
AND
LIDA LEE TALL
PRINCIPAL OF THE MARYLAND STATE NORMAL SCHOOL
TOWSON, MARYLAND
GINN AND COMPANY
BOSTON • NEW YORK • CHICAGO • LONDON
ATLANTA • DALLAS • COLUMBUS • SAN FRANCISCO
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Bdcc^T//^, J^/ j^
v:^
MityATi tciooL or t ducatmI
HarvardxUnivpfgity,
Library of theGi^duate School
of^mjcation
COPYRIGHT, 1920, BY
GEORGE A. MIRICK, FRANK W. BALLOU
, AND LIDA LEE TALL
ALL RIGHTS RESERVED
221.6
GINN AND COMPANY • PRO-
PRIETORS • BOSTON • U.S.A.
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PREFACE
There are difficulties that retard the progress of children in their
study of arithmetic \^hich until recently were not recognized and
are now too little considered by teachers. Dr. Charles H. Judd,
in his report on the Survey of the St. Louis Public Schools, points
to those in abstract arithmetic in these words :
It is a mistake to assume, for example, that addition is a single
process in all of its different applications. The fact is that addition
and all of the other arithmetical operations are among the most com-
plex subjects in the course of study. Children have a great deal of
difficulty with arithmetic because teachers do not understand the
special difficulties which are encountered by individual children at
different stages of their training.
In " How to Teach," by Strayer and Norsworthy, attention
is called to this matter, as follows:
Investigation seems to give evidence that in the habit of simple
column addition eight or nine different functions are involved, each
of which involves the use of several bonds. Besides these positive
connections a child in learning must inhibit other connections which
are incorrect, and these must often outnumber the correct ones. And
yet column addition has always been treated as a simple habit, with
perhaps one element of complexity, when carrying was involved. It
is evident that if the habit concerned does involve eight or nine
different functions, a child might go astray in any one.
The mental difficulties that children meet in their study of
arithmetic are not confined to abstract calculation. There are
complexities no less troublesome when they solve problems.
iii
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iv PRACTICE EXERCISES IN MENTAL ARITHMETIC
They must understand the situations in which the problems lie ;
they must exercise mathematical judgment to determine the
processes to be used, and in many instances to choose one of
two or three possible methods of solution ; they must interpret
the meaning of the language with which the problem is stated.
It seems to the authors that these parallel lines of difficulty
are best overcome by giving special training in meeting each
kind separately. Thiey also believe that systematic training in
both lines should begin not later than the third grade, that it
should deal with the simple, fundamental arithmetical facts and
the common types of problems, and that this training should
have for its purpose the development of mathematical facility
and skill.
The following characteristics of this book are in harmony
with these convictions:
1. The exercises in abstract calculation have been separated from
the exercises in problem solving, a page of the one following a page
of the other.
The relation between the two series of exercises is close, in that
the problems of each exercise involve the processes and combinations
studied on the preceding page of abstract exercises, except the two
pages of miscellaneous problems placed at the end of each quarter's
work.
2. All the whole-number combinations essential to success in
elementary arithmetic have been included in these exercises.
3. Repeated reviews of troublesome combinations are provided
according to their relative degree of difficulty.
4. To guide teachers in the use of the exercises detailed direc-
tions are to be found on nearly every page.
5. The problems on each page deal with one familiar situation
(except in the case of the miscellaneous problems). This leads to
more sustained thinking in each phase of the daily life in which
arithmetic is applied.
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PREFACE V
6. The problems have been stated in all the different ways in
which children are likely to meet them. Language difficulties have
been carefully removed.
7. Emphasis is placed on the making of original problems by the
pupils themselves. This exercise will train them to study their sur-
roundings, to see their school arithmetic in its everyday use, and
to apply their knowledge and skill gained in school to situations
out of school.
The authors wish to acknowledge their indebtedness to
Dr. Harry V. HoUoway's " Experimental Study to Determine
the Relative Difl&culty of the Elementary Combinations in
Addition and Multiplication." This study was made in 1918
and 1914, under the direction of the School of Education of
the University of Pennsylvania, and its findings have .been used
as a guide in the selection of troublesome combinations.
The authors are under obligation, also, to the superintendents
of the schools of Boston, of Cambridge, and of Arlington,
Massachusetts, for permission to make trial of the exercises in
the schools under their direction, and to the ^teachers who used
with their pupils the first prepared exercises. In the light of
these trials with a large number of pupils the exercises have
been thoroughly revised.
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CONTENTS
PAGE
Suggestions to Teachers xi
GRADE III. FIRST SERIES
EXERCISES
I-III. Addition: Numbers 0-9 2
IV. Problems : At Home (Addition) 3
V-VII. Addition : One and Two-Figure Numbers, Sums to 20 . . . 4
VIII. Problems : At Home (Addition) 6
IX-XI. Subtraction : Numbers 0-9 6
XII. Problems : At Home (Subtraction) 7
XIII-XV. Subtraction: Numbers 0-19 8
XVI. Problems : At Home (Subtraction) 9
XVII-XIX. Multiplication : Numbers 1-10 10
XX. Problems : At Home (Multiplication) 11
XXI-XXIII. Division : Even Quotients, Dividends to 100 12
XXIV. Problems : At Home (Division) 13
XXV. Problems : Miscellaneous 14
XXVI. Problems: Miscellaneous 15
GRADE III. SECOND SERIES
I-III. Addition : By Endings, No Carrying 16
IV. Problems : At Play (Addition) 17
V-VII. Addition : Review, Troublesome Combinations 18
VIII. Problems : At Play (Addition) 19
IX-XI. Subtraction : By Endings, No Borrowing 20
XII. Problems : At Play (Subtraction) 21
XIII-XV. Subtraction : Review, Troublesome Combinations 22
XVI. Problems : At Play (Subtraction) 23
XVII-XIX. Multiplication : Products to 100 24
XX. Problems : At Play (Multiplication) 25
XXI-XXIII. Division : Divisors 2-9, Dividends to 100 26
XXIV. Problems : At Play (Division) 27
XXV. Problems: Miscellaneous 28
XXVI. Problems: Miscellaneous 29
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viii PRACTICE EXERCISES IN MENTAL ARITHMETIC
GRADE III. THIRD SERIES
BXSBCI8BS PAGB
I-III. Addition : Two-Figure Numbers 30
IV. Problems : At School (Addition) 31
V-VII. Subtraction : Two-Figure Numbers 32
VIII. Problems : At School (Addition) 83
IX-XI. Addition: Two-Figure Numbers 34
XII. Problems : At School (Addition) 36
XIII-XV. Subtraction : Two-Figure Numbers 36
XVI. Problems : At School (Subtraction) 37
XVII-XIX. Multiplication: Remew 38
XX. Problems : At School (Multiplication) 39
XXI-XXIII. Division: ReHew 40
XXIV. Problems : At School (Multiplication) 41
XXV. Problems: Miscellaneous 42
XXVI. Problems : Miscellaneous 43
GRADE III. FOURTH SERIES
I-III. Addition : United States Money, Two-Figure Numbers . . 44
IV. Problems : Earning, Saving, and Spending (Addition) ... 46
V-VII. Addition : United States Money, Two-Figure Numbers . . 46
VIII. Problems : Earning, Saving, and Spending (Addition) ... 47
IX-XI. Subtraction : United States Money, Two-Figure Numbers . 48
XII. Problems : Earning, Saving, and Spending (Subtraction) . 49
XIII-XV. Multiplication : United States Money, One- and Two-Figure
Numbers 60
XVI. Problems : Earning, Saving, and Spending (Multiplication) . 61
XVII-XIX. Multiplication : United States Money, Troublesome to 12 x 9 52
XX. Problems : Earning, Saving, and Spending (Multiplication) . 63
XXI-XXIII. Division : Even Parts of Cents 54
XXIV. Problems : Earning, Saving, and Spending (Division) ... 56
XXV. Problems: Miscellaneous 66
XXVI. Problems: Miscellaneous 67
GRADE IV. FIRST SERIES
To Teachers 68
Tables op Measurements 69
I. Reading Numbers : 100-999 60
II, III. Addition : Three One-Figure Numbers 60
IV. Problems : At Home (Addition) 61
V. Reading Numbers : I-L 62
VI, VII. Addition : Three One-Figure Numbers 62
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CONTENTS
IX
BZBBCISES PAGE
VIII. Problems : At Home (Addition) ........... 63
IX. Counting : By 2's, 3's, 4's, 6's, to 100 .... ^ .... 64
X, XI. Subtraction : Beview by Endings 64
XII. Problems : At Home (Subtraction) 65
XIII. Reading Numbers : United States Money to $10 66
XIV, XV. Multiplication : Review, Easily Forgotten Combinations . . 66
XVI. Problems : At Home (Multiplication) 67
XVII. Reading Numbers : United States Money to |100 .... 68
XVni, XIX. Multiplication : By 10, 20, 100, etc 68
XX. Problems : At Home (Multiplication) 69
XXI. Reading Numbers : United States Money to |1000 .... 70
XXII, XXIII. Division : Divisor and Dividend Ending in Zero .... 70
XXIV. Problems : At Home (Division) 71
XXV. Problems: Miscellaneous 72
XXVI. Problems: Miscellaneous 73
GRADE IV. SECOND SERIES
I. Reading Numbers : 1000-5000 74
II, III. Addition : United States Money to |10 74
IV. Problems : At School (Addition) 75
V. Reading Numbers : LI-C . ^ 76
VI, VII. Addition: United States Money to $100 . 76
VIII. Problems : At School (Addition) 77
IX. Counting by 6's and 7's to 100 78
X, XI. Subtraction : Troublesome Combinations 78
XII. Problems : At School (Subtraction) 79
XIII. Counting : By 8's and 9's to 100 80
XIV, XV. Multiplication : Review 80
XVI. Problems : At School (Multiplication) 81
XVII. Counting : By ll's and 12's to 100 82
XVIII, XIX. Multiplication : Review 82
XX. Problems : At School (Multiplication) 83
XXI. Reading Numbers : Common Fractions 84
XXII, XXIII. Division : Two Types of Division 84
XXIV. Problems : At School (Division) 86
XXV. Problems: Miscellaneous 86
XXVI. Problems: Miscellaneous 87
GRADE IV. THIRD SERIES
I. Reading Numbers : Mixed Numbers 88
II, III. Fractional Parts : i, J, J of Numbers to 100 88
IV. Problems : At the Newsdealer's Store 89
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PKACTICE EXEECISES IN MENTAL ARITHMETIC
EXERCISES
V. Counting:
VI, VII. Measures :
VIII. Problems:
IX. Counting:
X, XI. Measures :
XII. Problems:
XIII. Measures :
XIV. Measures :
XV. Measures :
XVI. Problems:
XVII. Measures:
XVIII, XIX. Measures:
XX. Problems:
XXI. Measures :
XXII. Measures :
XXIII. Measures :
XXIV. Problems:
XXV. Problems:
XXVI. Problems:
PAGE
By Halves and Thirds to 10 90
Length 90
At the Dry-Goods Store 91
By Fourths and Fifths to 10 92
Areas 92
At a Hardware Store 93
Solids 94
Liquids 94
Dry Substances 94
At the Provision Store 96
Weight 96
Time 96
At the Balieshop 97
Counting 98
Paper 98
United States Money 98
At the Stationery Store 99
Miscellaneous 100
Miscellaneous 101
GRADE IV. FOURTH SERIES
I. Two-Process Examples : Addition and Subtraction . . . 102
II, III. Addition : Four One-Figure Numbers 102
IV. Problems of the Conductor 103
V. Two-Process Examples : Addition and Subtraction . . . 104
VI, VII. Addition : Five One-Figure Numbers 104
VIII. Problems of the Post Office 105
IX. Two-Process Examples : + , — , and -=- 106
X, XI. Making Change : To |100 106
XII. Problems of the Fruit Seller 107
XIII. Two-Process Examples : +, — , x,and-=- 108
XIV, XV. Multiplication : United States Money 108
XVI. Problems of the Dairy 109
XVII. Fractional Parts : With Remainders 110
XVIII, XIX. Division : With Remainders 110
XX. Problems of the Carpenter Ill
XXI. Fractional Parts : With Remainders 112
XXII, XXIII. Division : With Remainders 112
XXIV. Problems of the Farmer 113
XXV. Problems: Miscellaneous 114
XXVI. Problems : Miscellaneous 116
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SUGGESTIONS TO TEACHERS
MENTAL AND WRITTEN AKITHMETIC
The term mental is not a very happy one when used to dis-
tinguish so-called mental arithmetic from written arithmetic.
Of course all arithmetic is in its origin mental. Writing has
no place in arithmetic except as a means of recording the results
of thinking and as a mechanical help to thinking when the com-
putations are too complex for the mind to perform unaided.
Mental arithmetic and oral arithmetic are terms that are often
used synonymously to designate that kind of arithmetical work
that is done without the help of pencil, pen, or crayon. It is in
this sense that mental is used in this book. All the exercises,
abstract and concrete, are to be done without the pencil.
There are two considerations relating to written arithmetic
that deserve the teacher's serious attention.
The first consideration is this: While writing is in theory
merely a mechanical aid to mental arithmetic, as a matter of
fact the act of writing does introduce new factors into the
mental processes. It seems to influence the mind to use long,
cumbersome, uneconomical ways of calculating, instead of the
short, economical ways employed in purely mental calculation.
This influence has been overlooked by teachers in the past;
it has even been strengthened too often by an insistence upon
long and elaborate "figuring" in all written work, although the
same examples when done mentally have been calculated in
simple, direct ways.
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xii PEACTICE EXERCISES IN MENTAL ARITHMETIC
This common practice is wrong and retards the development
of both accuracy and speed. Pupils should be trained to do all
written work, whenever it is possible, by the same methods of
thinking that they use in mental work.
The second consideration to be taken account of in written
arithmetic is this : In a comparison of the relative value of oral
arithmetic and written arithmetic it should be recognized that
the oral form of expression is a means of training ; it is not an
end in itself. While mental activity is fundamental to both
oral and written expression, it is the written form that is by
far the more used, and it is the form by which alone mathe-
matical progress may be made into advanced fields.
Therefore, while the oral expression is insisted on for the exer-
cises in this book, it is not for oral expression's sake ; the exer-
cises are devised to train pupils to use the fundamentals in
arithmetic so skillfully that their written work may be done
more easily and correctly. This oral efl&ciency should be "car-
ried over" into written work, a teaching task whose difficulty is
not generally recognized.
THE PURPOSE OF THIS BOOK
From the foregoing it will be seen that this book is not
intended to replace the regular textbook. It has a dijBferent
purpose. It is a supplement to it. In the regular textbook
the oral exercises are principally to give practice in the new
subject that has been taught. In this book all the exercises
are to give practice in what should be abeady famiUar, with
a view to developing mastery, skill, and facility.
For instance, the first exercises in this book involve combi-
nations that were learned doubtless in the first grade. From
the Contents it will be seen that the work throughout is review
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SUGGESTIONS TO TEACHEES xiii
so far as the number combinations are concerned. The methods
of calculation and of drill are new, and these should lead to
the laying of a solid arithmetical foundation.
From the foregoing it follows that this book, although used
quite independently of the regular textbook, will greatly enhance
the results from the use of the latter book.
THE ABSTRACT EXERCISES
The abstract exercises provide training in purely mental
computations to the end that each pupil may acquire a reason-
able degree of accuracy and speed (that is, proportioned to his
native ability) in the arithmetic of his daily needs and in the
arithmetic that is necessaiy to progress in mathematical study.
STANDARDS OF ACCURACY AND SPEED
If one should ask, "How accurate and how speedy should
this mastery be ? " the answer must be indefinite. The human
brain is not an absolutely accurate machine, and its memory-
is not perfect. The action of the mind is much affected by
weather, condition of health, either temporary or permanent,
and by immediate social or other surroundings. Moreover, as
noted previously, minds differ one from the other in their
ability to attain accuracy and speed and in memory. There is,
there can be, therefore, no absolute standard of mathematical
attainments to which all pupils should be forced.
Professor Thomdike has said on this point that for the simple
combinations in all the processes (that is, 6 + 7, 13 — 7, 9x3,
72 -*- 8), if a child can give his answers in three seconds there
is absolute control over the process, and the process can be
considered as under reflex controL
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xiv PRACTICE EXERCISES IN MENTAL ARITHMETIC
It has been clearly proved, not alone in reading but in arith-
metic, that slowness does not contribute to accuracy, but rather
retards its development. The effort to accelerate seems to inten-
sify attention. Perhaps a good general standard of speed is that
of good oral reading, allowing for individual differences of tem-
perament. In good oral reading, hurrying is avoided but a ready
and intelligent rendering of the text without hesitation Is desired.
In fact, these arithmetical combinations may be thought of as
constituting an arithmetical vocabulary. It is as desirable, even
as necessary, that pupils know the essential vocabulary in the
one subject as that they know it in the other, and to the same
degree of mastery.
USING THE ABSTRACT EXERCISES
1. It is a principle pretty well established in all lines of
human activity that short periods of intensive practice are
better in' developing skill than long periods. It is impossible
to make a hard-and-fast rule regulating the length of the
period, but it should be long enough to allow each pupil to
get some training. It therefore follows that the class should be
small, not over twenty pupils. If a class is larger than this it
should be divided into two groups for mental-arithmetic work.
In a small class a good deal can be accomplished in ten minutes.
2. Show the pupils what you want them to do and how you
want them to do it by going through the exercise for them.
In this showing-exercise use the speed that you wish the
pupils to use and give only the answers as they should be
given by the pupils ; that is, they should not say " 7 and 8
are 15," but looking at the combination they should say " 15,"
as they read a word without spelling it.
Show the pupils in this way with each new exercise.
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SUGGESTIONS TO TEACHERS xv
3. While one pupil is reciting, all the others in the class should
follow closely, watching for errors. If it is necessary to maintain
attention, call on them out of turn to " go on from there."
4. Let each exercise be repeated until the majority of the
class know and meet your standard.
5. From time to time have each pupil note on a piece of
paper the combinations on which he hesitates. These are for
private study. j
6. Subordinate speed to accuracy, but do not forget nor
neglect speed.
7. Practice should be varied by proceeding with the exercises
from right to left, and up and down in columns.
8. The pencil should not be used in these exercises except
as suggested in paragraph 5.
9. The suggestions for methods of thinking in connection with
the exercises should be faithfully followed and applied also in
all written work.
THE CONCRETE-PROBLEM EXERCISES
The problems in each quarter of the grade work deal with
one familiar situation. In the first quarter of the third grade
they relate to the home, in the second quarter to play, etc.
This plan has been adopted so that pupils may think consecu-
tively in one field of arithmetical application at a time. It is
believed that this both simplifies and intensifies the thinking
and prepares the pupils to study more intelligently the real sit-
uations about them when they are assigned the task of making
original problems.
It will be noted also that the problems on each page involve
the number combinations and the processes that have been
studied on the opposite page of abstract exercises. The problems
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xvi PRACTICE EXERCISES IN MENTAL ARITHMETIC
have been constructed to the end that pupils may become familiar
with the dijBferent varieties of statement of problems in addition,
subtraction, multiplication, and division.
These problems are not as difficult as most children of these
grades can do. They are not standards of difficulty. On the
contrary, like the abstract exercises, they are exercises to give
facility and skill in interpreting problems. Therefore, language
and number difficulties have been removed, and one process is
dealt with in each exercise but set in a variety of simple lan-
guage forms.
Two pages of miscellaneous problems are put at the end of
each quarter s work to give further and more varied problem
training.
MAKING ORIGINAL PROBLEMS
At the bottom of each page of problems is a suggestion that
pupils make and bring to the class problems similar to those
they have just solved. These problems should not be imaginary
but real problems that they . themselves discover in situations
similar to those they have just solved on the same page.
There are two reasons for studying real situations in this way.
In the first place, if pupils have had no actual experience with
the material described or dealt with in a problem, or in the
situation in which the problem is set, that problem is as abstract
as if the words were not used, but the figures only. You may
test this for yourself by attempting to solve problems in navi-
gation, astronomy, or any other field in which you are not
familiar. Your trouble and confusion will be caused by your in-
ability to picture the problem, and that inability will persist until
you have had a concrete (that is, a real, first-hand, conscious)
contact with the situation.
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SUGGESTIONS TO TEACHEKS xvii
In the second place, that contact must be a conscious one. It
is one of the lessons that we teachers have been slow to leam ;
namely, that mere personal contact does not give us a knowledge
of things. Our eyes do not see, our ears do not hear, our mind
does not think about things until it begins to study them with
a purpose. Children go year after year to the post office without
being conscious of the peculiar nature of the post office. Country
children live in the . midst of nature without seeing nature.
City children Hve under the shadow of tall skyscrapers with-
out realizing what casts the shadow.
So the making of original problems, if the data for them are
those actually discovered in a purposeful study of real situa-
tions, will open the minds of the pupils to their surroundings
and will give them training in stating the problems they find
there. Both of these values are fundamental in developing skill
in solving problems.
THE USE OF THE PKOBLEM EXERCISES
1. Let the entire page of problems be assigned to the class
for silent reading.
2. The first lesson in class may be an oral reading and
discussion lesson without reference to problem solving. The
purpose is to understand the meaning of the problems and
to exchange experiences relating to other similar situations.
The character of the problems will lead to this discussion, it
is hoped.
3. Now take the problems one by one. Each may be read
again, orally or silently, as the teacher decides. The purpose now
is to have the pupil see clearly and state (a) what is to be done
and (J) the answer.
Of course the pencil will not be used.
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xviii PRACTICE EXERCISES IN MENTAL ARITHMETIC
4. If the pupil makes a mistake in (a) or in (6) do not resort to
explanations and questions ; allow him to sit down and think it
out by himself while the class proceeds with the next problem.
Note. Pupils think logically. Their minds are so made that logical
thinking is their natural way of thinking. But the ability to state reasons,
to give and understand "explanations," — that is, the if*s, ancTs, thens,
therefore' s, because' s, — develops after childhood has passed.
To put the matter in another way, the mind tends to act correctly in
determining the process that should be applied- in a given problem once
the problem situation is understood. There need be, then, but an abundance
of practice in dealing with word problems involving familiar situations to
produce quickness and accuracy in this mental reaction.
5. Encourage and reward the use in written problems of
methods of solution and of computation employed in mental
exercises.
MATHEMATICAL JUDGMENT
Those who use numbers skillfully are constantly employing
what may be called a calculation or a computation judgment.
One out of many possible cases will illustrate this.
Problem. At $0.12^ each, what do 10 handkerchiefs cost ?
There is no doubt here about the process to be used.
$0.12J is to be multiplied by 10. But there are at least three
possible ways of making the calculation.
(1) $0.12^ (2) $0.12i = $0,125 (3) $0.12^
^Q $0,125 X 10 = $1.25 $0.25 x 5 = $1.25
5
^ ork (Multiplication by moving (Multiplying by the
.. decimal point.) factors of 10.)
$l.^o
This, it is evident, is a matter of calculation judgment The
question is which of three possible ways of multiplying is best
in this particular case.
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SUGGESTIONS TO TEACHEES xix
To answer the question the pupil must have facility in using
the different methods and readiness in applying each according
to the conditions in given cases. This readiness and facility
can come only with practice, and this practice should begin
early. It is provided for in this book.
There is another need for judgment in determining the best
process to apply in a given case. To illustrate :
Problem. If one handkerchief costs $0.12]^, how many can be
bought for $1.50 ?
Here there is a question of what process rather than of how
to carry out the process. It is a question of how to solve the
problem rather than of how to compute.
This problem may be solved by division, or by division and
addition.
(1) 11.50 H- $0.12^ = (2) $0.12^ = $f
♦0.125) $1.50 Then 8 handkerchiefs may be
(or) bought for $1.00, and 4 handker-
41 Kf) ^ = chiefs for $0.50. Therefore 12 may
* ^ $0.25 "" be bought for $1.50.
As in the case of calculation judgment this process or problem
judgment develops with a knowledge of alternative methods of
solution and with practice in applying different methods to the
same problems until the judgments are made easily and quickly.
Training to this end should not be delayed too long, for
clumsy and troublesome habits of work will become fixed, as
they are fixed in the minds of so many school children to-day.
A beginning of training in this kind of judgment is made in
connection with many problems in this book.
•There is a third kind of mathematical judgment that chil-
dren should be trained to use. It is involved in answering the
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XX PRACTICE EXERCISES IN MENTAL ARITHMETIC
question, " Is my answer reasonable ? " If the minds of pupils
are properly alert they will frequently ask: "Is this problem
reasonable ? Are the prices and quantities stated in the prob-
lem such as are likely to occur in real problems ? "
Incentives to exercise this kind of judgment are scattered
through this book, and it is hoped that teachers will make use
of them. Additional opportunities for judging the reasonableness
of the problems and of problem answers are given in the original
problems that the children themselves make and bring to class.
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PRACTICE EXERCISES IN
MENTAL ARITHMETIC
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GRADE III. FIRST SERIES
Note. Pupils should be trained to state the sums at the same rate of
speed as they read familiar text. See Suggestions to Teachers.
I. >
A^DDITIOm
1
A. 2
1
1
1
1
6
1
4
1
1
3
9
7
1
1
5
1
8
B. 2
2
5
2
2
2
8
2
3
2
6
2
7
9
3
2
4
3
II.
ADDITION
A. 5
3
4
3
6
3
4
4
7
3
7
3
8
3
9
4
9
4
B. 4
8
4
7
5
5
9
5
6
5
4
6
5
5
6
5
8
6
III.
ADDITION
A. 9
6
8
7
9
7
8
9
9
6
7
6
7
7
8
8
8
9
B. 1
2
3
5
9
1
2
4
6
C. 8
6
7
8
6
8
5
9
7
9
8
9
5
9
7
7
4
6
D. 5
4
9
8
8
4
7
6 .
6
9
7
3
3
8
8
3
4
5
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GRADE III. FIRST SERIES 3
IV. PROBLEMS; AT HOME
1. In John's family there are 4 people. One day 3
friends come to dinner. How many plates should mother
put on the table that day for dinner?
2. Usually John takes 5 minutes to get ready for
dinner, but he spends 2 minutes more the day the visitors
come. How long does he take that day ?
3. It is a part of Susan's work at home to sweep the
front and back steps each day. There are 6 front steps
and 5 back steps. How many steps does she sweep?
4. How many stockings will mother mend if she finds
that John has 3 stockings with holes in them and Susan
has 3 stockings with holes in them?
5. There are 7 rugs on the floors upstairs and 8 rugs
on the lower floor in John's home. If he cleaned them
all, how many would be clean?
6. Susan's father decides to buy new curtains for the
kitchen and for the dining room. How many ciu'tains
will be required for the 5 windows of the kitchen and
the 3 windows of the dining room ?
7. If John has 8 books in his library and Susan has
9 books in her library, how many books do they have
together ?
8. How many rolls does mother make when she bakes
9 in one pan and 6 in another pan?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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4 PEACTICE EXERCISES IN MENTAL ARITHMETIC
Note. Train pupils to recognize the total sums at a glance, that is,
12 + 6 = 18 ; no/ 2 + 6= 8, and 1 ten = 18. These are really a review of
Exercises I-III.
V. ADDITION
A. 1
2
1
11 3 12
7
3
12
10
10
11
2 16 4
10
12
5
5
17
15
15
14
12
12
13
3
13
_2
3
5
_4
2
_6
_3
14
VI. ADDITION
A. 15
11
12
5 6 2
3
16
13
4
9
7
14 14 15
17
2
2
B. 16
13
9
11
14
1
13
14
_0
4
19
10
4
2
19
7
a 16
13
14
16
2
14
13
2
15
4
_5
5
3
13
3
6
14
J
VII. ADDITION
^.10 + 10= 4 + 15= 18 + 2= 4 + 13 =
5. 12 + 8= 13 + 5= 15 + 5= 4 + 16 =
C. 12 + 1= 18 + 0= 13 + 6= 18 + 2 =
D. + 20= 13 + 4= 2 + 17= 16 + 3 =
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GEADE ni. FIEST SERIES 5
VIII. PROBLEMS: AT HOME
1. Samuel fills his mother's wood box every morning.
One morning he filled it by carrying 9 sticks at one trip
from the woodshed and 11 sticks at another trip. How
many sticks filled the box?
2. How many minutes does Mary work when she helps
her mother for 10 minutes washing the dinner dishes and
5 minutes setting the table ?
3. If Samuel has 6 cents of his own in his pocket and
his mother gives him 12 cents with which to do an errand,
how much money does he carry to the store ?
4. Mary is asked to dust all the chairs in the living room
and dining room. There are 3 rockers and 11 other chairs.
How many chairs are there to be dusted ?
5. One day Mary puts her mother's workbasket in order.
Sbe finds 12 spools of white thread and 5 spools of colored
thread. How many spools are in the basket ?
6. If 5 one day after school out in the orchard, Sam picks
up 8 quarts of pears and Mary picks up 12 quarts, how
many quarts of pears do both children pick up?
7. When mother has put up 13 jars of peach preserves
and 6 jars of cherry preserves, how many jars will she
have for winter?
Additional Work. Each pupil should write out and bring to class
a similar problem of his oum.
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6 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. Pupils should state the answers without repeating the numbers
that are to be subtracted. See Suggestions to Teachers.
IX. SUBTRACTION
A. 2
3
9
7
1
1
6
5
4
1
1
1
1
1
1
1
1
B. 2
6
2
7
9
5
8
4 •
3
2
2
2
2
2
2
2
2
X. SUBTRACTION
^. 3
3
5
3
7
3
4
3
8
3
6
3
9
3
10
4
4
B 5
5
9
4
7
4
5
4
8
4
10
2
10
6
6
4
7
5
XL SUBTRACTION
A. 6
9
8
6
9
7
8 7 7
5
5
5
6
6
6
6 7
B. 9
8
10
9
9
10
10 10 .10
7
7
8
8
9
5
3 7 10
a 8
7
6
3
4
5
6 5 7
3
4
5
2 3 4
D. 9
6
5
7
8
9
7 9 9
5
4
2
3
5
4
5 7 2
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GRADE III. FIRST SERIES 7
XII. PROBLEMS: AT HOME
1. Mother finds that she has 9 eggs. She uses 2 eggs
in a cake. How many are left?
2. Hannah is sent to the store to buy a yeast cake.
She is given 5 cents, and the yeast cake costs 2 cents.
What change should she bring back?
3. If Hannah sets the supper table for 7 people and
only 5 people come to supper, how many empty places
are there?
4. Harry can walk to the store from his home in
8 minutes, but when his mother wants an errand done in a
hurry, he can run there in 5 minutes. How many minutes
does he save by running ?
5. How much taller is Harry's father, who is 6 feet tall,
than Harry, who is 3 feet tall ?
6. There are 10 napkins to be laundered. When mother
has laundered 3 of them, how many remain to be done ?
7. Mother asks Hannah to pour 3 pints of milk into a
bowl that will hold 8 pints. How many more pints will it
take to fill it after Hannah has poured in her milk ?
8. In the dining room there are 6 chairs. The family
uses only 4 of them at breakfast time. How many chairs
are unused at breakfast ?
9. How many handkerchiefs has Harry after he has
lost 2 from the 9 that he had after last Christmas?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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8 PEACTICE EXERCISES IN MENTAL ARITHMETIC
Note. The exercises on this page give training in recognizing differences
within the limits 11-10 in the minuend and 0-10 in the subtrahend.
XIII. SUBTRACTION
A. 11 11 12 11 12 11 12 14 11
B. 11 12 15 11 11 12 11 12 13
XIV. SUBTRACTION
A. 14 14 13 12 14 14 13 13 14
455769647
B. 13
14
15
14
13
14
15
13
15
7
_9
_7_
_]_
9
_8
_9
8
_6
C. 16
17
18
19
19
17
19
15
15
_2
5
2
7
3
2
4
3
2
XV. SUBTRACTION
^.15-8= 16-7= 17-8= 18-10 =
i?. 16-9= 13-0= 18-3= 16-8 =
C 18-4= 17-3= 18-9= 19-6 =
D. 17-4= 19-2= 18-4= 19-5 =
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GEADE III. FIRST SERIES 9
XVI. PROBLEMS: AT HOME
1. There are 14 days in 2 weeks. Of these 14 days
children go to school 10 days. How many days in
2 weeks do children have no school?
2. Sarah invited 10 friends to her doll's party, but 4
of them could not come. How many came?
3. For the party Sarah counted out 18 lumps of sugar.
Of these one dozen lumps were eaten. How many lumps
were left?
4. What is the difference between Frank's age and
Sarah's age if Frank is 9 years old and Sarah is 16
years old?
5. Sarah has 19 cents in her bank. She takes out the
19 cents to spend for a birthday present for her mother.
How much is left in the bank ?
. 6. It is Frank's work to keep the front walk clean.
The walk is 18 feet long. After he has swept 12 feet
of it, how many feet remain to be swept?
7. Mother buys 16 quarts of apples. She uses some
for cooking and she gives some to the children. There
are 7 quarts left. How many quarts were used ?
8. The children have a party for which mother makes
17 pop-corn balls. After the party there are 5 pop^jom
balls left. How many were eaten?
Additional Work, Each pupil should write out and bring to class
a similar problem of his own.
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10 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. Pupils should be trained to recognize (without conscious calcu-
lation) these products. They should become familiar with the fact that
the product is the same whichever term is used as multiplier. For addi-
tional practice these exercises may be copied or written on the board,
reversing the terms.
XVII. MULTIPLICATION
A. 1
1
2
1
3
1
2
2
3
2
10
_2
6
2
4
2
3
3
B. 5
2
8
2
9
3
4
3
7
2
5
3
9
2
7
3
10
1
XVIII. MULTIPLICATION
A. 4
4
6
3
5
4
8
3
9
4
5
5
6
4
9
5
7
4
B. 6
5
8
4
7
5
6
6
8
5
9
6
7
6
7
7
8
6
XIX. MULTIPLICATION
A 7x8= 10x10= 9x9= 8x8 =
5. 2x10= 8x9= 1x7= 7x9 =
C. 5x1= 1x5= 5x10= 10x5 =
i). 3 x 10 = 4 X 10 = 9 X 10 = 10 X 8 =
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GRADE III. FIRST SERIES 11
XX. PROBLEMS: AT HOME
1. Peter saves 3 cents a week for 7 weeks. How much
mone;^ does he then have ?
2. How many doll's dresses has Frances if she has 4
dolls and each doll has 4 dresses?
3. In the doll house there are 3 rooms. In each room
there are 2 chairs. How many chairs are there in the
doll house?
4. How much money should Frances take with her to
the store when she goes to buy 6 buns at 2 cents each?
5. Mother has made 2 pats of butter to show you how
to make them. She asks you to make 9 times as many.
How many will you make ?
6. Peter has a garden. He gives mother 1 bunch of
radishes from it each day for a week. How many bunches
does he give her ?
7. If there are 5 people in a family and each one eats
3 rolls for breakfast, how many rolls must be baked for
breakfast ?
8. Frances wants to make a string of beads for each
of her 4 dolls. She finds that 10 beads will make a very
good string. How many beads does she need?
9. There are 8 chairs in the dining room. Each chair
has 4 legs. How many legs have all the chairs together ?
Additional Work. Each pupil should write out and bring to class
a similar problem of his otvn.
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12 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. Quotients should be recognized without conscious calculation,
as in previous exercises. The teacher will note that in the following
exercises the dividends are the products in the preceding multiplication
exercises. For additional practice the dividends may be copied on the
board, using for divisors the quotients in the following exercises.
XXI. DIVISION
A. 1)1
1)2
1)3
2)4
2)6
2)20
B. 2)12
2)8
3)9
2)10
2)16
3)27
a 3)12
2)14
3)15
2)18
3)21
1)10
XXII. DIVISION
A. 4)IQ 3JIS 4)20 3)24 4)36 5)25
B. 4)24 5)45 4)28 5)30 4)32 5)36
a 6)36 5)40 6)54 6)42 7)49 6)48
XXIII. DIVISION
A. 56-1-7= 100-!- 10 =
5. 20-!- 2= 72-»-8 =
C. 5h-5= 5-i-l =
D. 30-^3= 40-»-4 =
81-!- 9 =
64-!- 8 =
7-»-l =
63-^7 =
50-!- 5 =
50-h10 =
90-^9 =
80-^8 =
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GKADE III. FIRST SERIES 13
XXIV. PROBLEMS: AT HOME
1. Mother wants to divide 9 pieces of candy among
her 3 children. How many pieces shall she give to each
child?
2. Harry has in his garden a row of peas 18 feet long.
He plans to weed it during the next 6 days. How many
feet should he weed each day ?
3. There are 14 children at play. They counted off
into 2 equal groups. How many children were in each
group?
4. If the 14 children had counted off into 7 equal
groups, how many would have been in each group?
5. Harold and Barbara had 2 children come to play'
with them. Mother gave them a dozen apples. If the
apples were divided equally among the children, how
many would each have?
6. The children were helping mother make sandwiches
for a picnic. After a while she counted and said : *' There
are 20 sandwiches, and there will be 5 people. I wonder
if it is enough." How many could each person have?
(Do you think that would be enough?)
7. Mother's biscuit pan holds 18 biscuits. There are
3 long rows of biscuits in the pan. How many in each
long row?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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14 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XXV. PROBLEMS: MISCELLANEOUS
Note. This lesson introduces what may be called the "completion type "
of problem. The correct number should be read at the dash.
1. Mother said to Rebecca: *' There are 7 in our family
and we shall have 12 guests on Thanksgiving Day. If
they all come we must set the table for people."
2. Father said: "For our own family a 6-pound turkey
would be big enough, but if the other 12 people come we
shall need a turkey 3 times as big. That will be an
pound turkey."
3. For the Thanksgiving dinner mother baked 4 loaves
of bread. She said, "If I cut each loaf into 10 slices, I
shall have slices of bread." (Do you think that
would be enough?)
4. Rebecca promised to make a place card for each
of the 19 people that were expected at the Thanksgiving
dinner. The day before Thanksgiving she found she had
made only 9 of them. So she set to work to make the
other cards.
5. Of the 19 people expected at dinner 2 sent word
that they could not come. So the table was set for
people.
6. To decorate the table father brought home the day
before Thanksgiving 6 red roses and 9 white roses. This
made flowers for the table.
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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GRADE III. FIRST SERIES 15
XXVI. PROBLEMS: MISCELLANEOUS
1. Tom and Sam are building a playhouse of some
bricks. Tom says, " I can carry 5 bricks at once." Sam
says, '* I can carry 3 more than that." How many can
Sam carry?
2. Sarah picked 13 roses from a rosebush. She gave
7 of them to her mother. How many did she keep
for herself?
3. If Sarah wanted to make 12 Christmas presents
and finished 7 of them in November, how many were
left to be made in December?
4. One week in the fall Tom spent 1 hour each day
for 6 days raking up the leaves around the house. On
counting it up he found that he had worked hours
raking leaves.
5. Sarah spent 15 minutes sewing buttons on her doll's
dress. In that time she sewed on 3 buttons. About how
long did it take her to sew on 1 button ?
6. It is Tom's work to keep his mother supplied with
kindling wood. His father buys wood in sticks 4 feet
long. If Tom saws these sticks into 4 pieces each, how
long is each piece?
7. Tom finds that when he has sawed 5 sticks into
4 pieces each he has pieces.
8. Mother asks Sarah to find how many handkerchiefs
she and Tom have. She finds 8 of Tom's and 7 of her own
and reports that together they have handkerchiefs.
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GRADE III. SECOND SERIES
Note. Practice is here given in "addition by endings"; that is, in not-
ing that the sum of two units is the same irrespective of the tens with which
they may stand. Other combinations may be made for further practice on
the board.
I. ADDITION
A. 10
1
20
1
30
J.
42
_1
52
1
62
1
7
2
17
2
27
_2
B. 37
2
47
2
77
2
6
2
16
2
26
2
7
3
17
3
87
II. ADDITION
A. 5
_3
15
3
25
3
95
3
3
3
23
3
63
3
6
_4
26
4
B. 56
_4
5
_4
75
4
85
4
4
5
14
5
24
_5
3
5
43
5
III. ADDITION
A. 73
5
3
6
53
_6
83
_6
2
6
12
6
22
_6
3
7
33
7
B. 43
J_
10
7
20
7
30
7
11
8
21
8
31
_8
10
_9
20
9
C. 6
3
16
13
26
23
16
53
5
14
15
34
25
64
3
1
13
11
D, 23
31
13
81
6
2
26
22
36
42
6
92
15
12
15
42
25
62
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GRADE III. SECOND SERIES 17
IV. PROBLEMS: AT PLAY
1. At the beginning of the marble season Peter has
22 marbles. He buys 10 more. How many does he have
then?
2. If Horace has 32 marbles and buys 10 more, how
many does he have?
3. Ruth makes Peter a bag for his marbles. He puts
55 marbles in the bag. How many are in the bag after
he has put in 4 more?
4. If Peter had put in the bag 35 marbles first and
then 4, he would have had marbles in the bag.
5. How much money did Horace spend for marbles if
he spent 12 cents that his father gave him and 8 cents
that he earned?
6. Theodore spends 22 cents one day for marbles
and 8 cents the next. On both days he spends
cents.
7. Ruth likes to play marbles also. She buys 17 marbles
and Peter gives her 2. She then has marbles.
8. If Horace gives her 2 marbles one day when she has
37, how many marbles does she have?
9. When the end of the marble season comes Peter
counts his marbles and finds that he has 3 green and 13
yellow ones, or in all.
Additional Work. Each pupil should tmrite out and bring to class
a similar problem of his oum.
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18 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. The following are review exercises of the more troublesome
combinations. Pupils should practice until they recognize these sums
as readily as the easier ones, for on this readiness depends success in
succeeding exercises.
V. ADDITION
A.
6
6
9
7
6
4
7
8
6
2
6
4
9
8
6
6
3
9
B.
3
8
9
5
3
6
9
5
7
4
5
9
9
2
5
2
7
2
VI. ADDITION
A.
4
5
" 4
6
1
8
9
8
7
8
4
7
3
7
7
3
9
3
B.
3
8
16
13
5
2
2
12
13
5
8
3
6
12
15
17
Jl
_5
C.
4
13
5
4
19
7
5
9
18
15
4
14
13
_8
18
17
16
5
VII. ADDITION
A 16 + 4= 14 + 6= 15 + 3= 17 + 2 =
A 3 + 17= 13 + 7= 17 + 7= 6 + 16 =
C. 4 + 15= 16 + 3= 2 + 16= 14 + 3 =
D. 18 + 6= 4 + 19= 7 + 16= 5 + 19 =
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GRADE III. SECOND SERIES 19
VIII. PROBLEMS: AT PLAY
1. Edith and Amy are jumping rope. Edith jumps 9
times and Amy jumps 4 times. They together jump
times.
2. How many jumps does Edith make in two trials if
on the first trial she jumps 8 times and on the second
trial 3 times?
3. The two girls have jump ropes of different lengths.
One is 5 feet long, the other 6 feet. If they were put end
to end, how long a rope would they make ?
4. Peter and Edith are playing jackstraws. After a
time Peter counts his pile and finds he has 12 straws.
Edith has 8 straws in her pile. How many straws have
they both drawn ?
5. Amy joins the game of jackstraws. If she draws
out 7 straws and afterwards 11 more, how many should
there be in her pile ?
6. Peter and Will decide to put their money together
to buy a baseball. Peter has 4 cents and Will succeeds in
finding 6 cents. How much do they both have ? (Is this
enough to buy a ball ?)
7. Some boys^are getting ready for a snowball fight.
They make 39 balls to use when they are attacked and
8 to throw at once. They then must have 'made in all
balls.
Additional Work. Each pupil Bhovld write out and bring to class
a similar problem of his own.
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20 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. The following are exercises in "subtraction by endings "; minu-
ends not exceeding 100, subtrahends not exceeding 9. Exercises do not
involve "borrowing."
IX. SUBTRACTION
A. 11 21 31 41 14 24 34 64 94
J.J.J.J._2_2_2_2^
B. 13 33 53 45 85 76 26 86 16
33.3 1 12 2 2 3
X. SUBTRACTION
A. 47 27 97 18 38 68 19 49 89
444555666
B. 39
59
19
27
57
87
28
58
18
4
_4
_4
5
_5
5
_6
_6
6
C. 98
78
48
29
19
69
55
15
25
_3
3
_3
5
_5
5
2
2
_2
XI. SUBTRACTION
^.19-7= 59-7= 99-7= 29-7 =
B. 19-S= 49 - 8 = 69 - 8 = * 19 - 8 =
a 29-9=' 89-9= 17-3= 27-3 =
i). 37 - 3 = 17 - 2 = 27 - 2 = 57 - 2 =
.e:. 16-4= 36-4= 19-3= 49-3 =
Digitized byCjOOQlC
GRADE III. SECOND SERIES 21
XII. PROBLEMS: AT PLAY
1. The children are playing store. Richard has in
his store 14 nails, 24 toothpicks, and 54 pins. If he
sells 3 of each of these, how many of each has he left?
2. Marion makes for her store 5 mud pies, 15 loaves of
bread, 35 rolls, and 25 cakes. She sells 4 of each of them
and has left pies, loaves of bread, rolls,
and cakes.
3. Richard puts some buttons that his mother has
given him in 4 piles according to size. In the first pile
are 9 buttons, in the second 29 buttons, in the third
69 buttons, and in the fourth 49 buttons. How many
are left in each pile if he sells 7 buttons from each?
4. Sarah makes 23 glasses of lemonade in one pail and
13 glasses of orangeade in another pail. After she has
sold 2 glasses from each pail she has left glasses of
lemonade and glasses of orangeade.
5. Henry sells stationery in his store. He has 39 sheets
of white paper and 59 sheets of yellow paper. Richard
buys 6 sheets of each kind. How much of each kind
does Henry have left?
6. Tom has in his store a pile of 88 beans, one of
38 peas, and one of 68 kernels of com. Sarah buys 5
from each pile. How much has Tom left in each pile?
Additional Work. Each pupil should write out and bring to class
a similar problem of his otm.
Digitized by VjOOQ IC
22 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. The following are review exercises of the more troublesome
combinations of minuends to 20 and subtrahends to 10. Pupils should
recognize them as readily as they do the easier ones.
XIII. SUBTRACTION
A. 5
3
9
4
8
3
7
2
10
4
7
5
7
4
9
2
7
3
B. 10
2
5
2
9
7
9
5
10
6
8
2
9
3
9
6
10
3
XIV. SUBTRACTION
A. 10
11
13
12
11
12
11
12
13
7
2
5
4
3
_3
4
5
4
B. 13
11
14
11
12
14
11
12
14
6
_5
_8
_6
7
6
7
8
_5
a 10
12
14
18
19
18
17
19
17
_5
6
_T_
_9
_4
3
2
2
5
XV. SUBTRACTION
^.12-9= 11-8= 13-7= 11-9 =
A 13-8= 15-6= 16-7= 17-8 =
a 14-9= 13-9= 14-8= 15-7 =
D. 17-9= 15-8= 16-9= 15-9 =
JS-. 13-6= 11-5= 13-5= 12-4 =
Digitized byCjOOQlC
GRADE III. SECOND SERIES 23
XVI. PROBLEMS: AT PLAY
1. In a potato race Luther misses 4 of the 12 potatoes
in his row. How many does he pick up ?
2. Susan picks up all of the 12 potatoes in her row,
but 3 of them fall outside the box into which she should
have dropped them. Therefore only potatoes are
counted for her.
3. If 5 rows of potatoes are laid out for the race,
but only 3 children take part, there are rows too
many.
4. There are 18 grown people present to see the race.
Of these 7 are men. How many women are there ?
5. If there are 9 children present and only 3 of
them take part in the race, there are children
who watch.
6. After the potato race how many grown people are
left if 5 of them go home?
7. A little later only 11 grown people are left; how
many have then gone home?
8. Of the 9 children only 7 are able to stay to a picnic
dinner. Then children are obliged to leave.
9. Four of the children at the dinner are boys. How
many, then, are girls?
Additional Work. Each pupil should write out and bring to class
Q, similar problem of his own.
Digitized byCjOOQlC
24 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. Exercises in recognizing (without conscious calculation) products
not exceeding 100 : multiplicands of two figures, multipliers to 9. Pupils
should recognize these products as readily as they do 2x3. These
exercises may be put on the board with the order of the terms reversed.
XVII. MULTIPLICATION
A. 11
12
13
14
15
20
21
22
23
_2
_2
_2
_2
2
_2
2
_2
2
B. 24
30
31
32
33
34
40
41
42
_2
_2
2
2
_2
2
2
2
2
XVIII. MULTIPLICATION
A. 43
44
11
12
13
20
22
23
30
2
2
3
3
_3
3
3
3
J
A 31
32
33
11
12
20
21
22
11
_3
3
3
4
_4
4
4
4
5
XIX. MULTIPLICATION
^. 11 X 5 = 12 X 5 = 11 X 6 = 12 X 6 =
A 11 X 7 = 12 X 7 = 11 X 8 = 12 X 8 =
C. 11 X 9 = 25 X 2 = 25 X 3 = 25 x 4 =
Z>. 50x1= 50x2= 35x2= 45x2 =
^. 10 X 1 = 11 X 1 = 22 X 1 = 44 X 1 =
Digitized byCjOOQlC
GRADE III. SECOND SERIES 25
XX. PROBLEMS: AT PLAY
1. Jerry can run around the house in 45 seconds, but it
takes his little brother twice as long. The little brother
runs around the house in seconds.
2. How many marbles has James if he has 3 times as
many as Warren, who has 20 marbles ?
3. While little Ethel is making 15 mud pies, her older
sister makes twice as many. How many does her sister
make ?
4. In Richard's play store 25 pebbles are called a
bushel of potatoes. How many pebbles must he collect
if he wants to have in his store 4 bushels of potatoes?
5. John has 23 marbles and so has each of his two
friends. How many marbles have they together?
6. Ethel, Jane, and Rose are playing dominoes. Ethel
counts 13 spots on the dominoes that she has left at
the close of the game, and Jane counts 3 times as
many on hers. How many does Jane count? Rose
counts on her dominoes twice as many spots as Ethel
does, or spots.
7. Hannah wants to buy a set of doll's dishes, but it
costs 3 times as much as she has, for she has only 25 cents.
What is the price of the dishes ?
Additional Work. Each pupil should write out and bring to class
a similar problem of Ms otun.
Digitized by VjOOQ IC
26 PRACTICE EXERCISES IN MENTAL ARITHMETIC
NuTE. Qaotients should be recognized without conscious calculation.
Divisors to 9 ; dividends to 100. These exercises are the reverse of Exer-
cises XVII-XIX.
XXI. DIVISION
A. 2)22 2)24 2)26 2)28 2)30 2)40
B. 2)42 2)44 . 2)46 2)48 2)60 2)62
C. 2)64 2)66 2)68 2)80 2)82 2)84
XXII. DIVISION
A. 2)86 2)88 3)33 3)36 3)39 3)60
5. 3)66 3)69 3)90 3)93 3)96 3)99
a 4)44 4)48 4)80 4)84 4)88 5)55
XXIII.
DIVISION
^.
55-s-5 =
60 + 5 =
66 + 6 =
72 + 6 =
5.
77-^-7 =
84+7 =
88 + 8 =
96 + 8 =
c.
99 H- 9 =
50 + 2 =
75 + 3 =
100 + 4 =
J).
50 + 1 =
100 + 2 =
70 + 2 =
90+2 =
E.
10 + 1 =
11 + 1 =
22+1 =
44 + 1 =
Digitized by Google
GRADE III. SECOND SERIES 27
XXIV. PROBLEMS: AT PLAY
1. Mother gives to Mary and her 4 friends an old
clothesline for jump ropes. It is 30 feet long. If the
clothesline is cut into equal lengths so that each girl
has one, how long will each rope be?
2. In Arthur's yard there is a pile of old bricks. He
counts them and finds there are 99 bricks in the pile.
He makes 3 houses of equal size of the bricks, putting
bricks into each house.
3. Eleanor's garden plot is square. It is 20 feet
around. Each side must then be feet.
4. Esther has 5 dolls at her doll-party. Mother gives
her 30 cakes, which she divides equally among her dolls.
How many cakes does each doll have?
5. If 3 boys pay equally for a kite string that costs
18 cents, each boy's share is cents.
6. The twine is 90 feet long. If the boys divided it
equally among themselves, each boy would have
feet of string. (Would this be enough for a kite
string ?)
7. How much money will Martha spend if she divides
75 cents her uncle gives her into 3 parts and spends
one of them?
8. Harriet has 25 cents, which she spends for little dolls
that cost 5 cents each. How many dolls does she buy?
Additional Work. Each pupil should write out and bring to class
a similar problem of his ovm.
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28 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XXV. PROBLEMS: MISCELLANEOUS
1. Two boys buy a football together. One gives 50
cents towards it, the other 25 cents. The ball costs
cents.
2. When the two boys come out of the store they
find 20 other boys waiting to play with them. That
makes boys ready for a game.
3. The boys are divided into 2 equal groups. That
makes two teams of boys each.
4. One side makes 12 points the first half, and the
same side makes 7 points the second half, or points
in all.
5. When the game is over, one side has made 30
points and the other side has made twice as many. How
many points has the other side made ?
6. While the boys are playing football the girls are
playing bean bag. There are at first 13 white bags and
3 blue bags, or bags in all.
7. Hattie joins the company and brings 4 white and
4 yellow bean bags. How many of each color do the
girls now have to play with?
8. Hattie scores 7 points, and on a second try she
scores 8 points. Her score then stands points.
9. Marion scores 8 points at first and then 8 points.
How many points has she then? (Do this in two ways.)
Additional Work, Each pupil should write out and bring to class
a similar problem of his ovm.
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GRADE III. SECOND SERIES 29
XXVI. PROBLEMS: MISCELLANEOUS
1. One beautiful fall day a number of children go
with their parents on a picnic. If there are 7 boys
and 7 girls, how many children are there ? (Do this in
two ways.)
2. Each boy takes a lunch basket in each hand. There
must have been baskets in all, for the parents had
packed their lunches in the children's baskets.
3. Twenty people sat down to lunch. As there were
14 children, there must have been parents.
4. It was found that 4 children had brought 3 apples
apiece. So there were apples for luncheon.
5. If there were 26 ham sandwiches and 16 chicken
sandwiches, how many more were there of the ham than
of the chicken sandwiches?
6. Each of the 14 children ate 2 olives. How many
olives were eaten by the children ? (Do this in two ways.
Which way is easier?)
7. There were 6 olives left. The parents ate these,
each having the same number. How many did each of
the 6 parents have ? (Do this in two ways. Which way
is easier ?)
Additional Work. Each pupil should write out and bring to class
a similar problem of his otvn.
Digitized by VjOOQ IC
GRADE III. THIRD SERIES
Note. These exercises give practice in recognizing at a glance the sum
of two-figure numbers. Pupils should give the sums without naming the
numbers.
I. ADDITION
A. 10
20
30
40 50 35
25
25
10
10
20
30
40 50 35
25
75
11
B. 11 12 13 14 15 10 10 10 10
111213141512131415
II. ADDITION
A. 10 10 10 10 10 10 10 10 10
16 17 18 19 20 30 40 50 60
B. 10
10
10
20
20
20
20
20
20
70
80
90
30
40
50
60
70
80
C. 22
33
44
21
31
41
32
33
34
22
33
44
21
31
41
32
33
34
III. ADDITION
A. 30 + 40 = 30 + 50 = 30 + 60 = 30 + 70 =
B. 40 + 50 = 40 + 60 = 11 + 12 = 11 + 13 =
a 11 + 20= 11 + 14= 11 + 22= 11 + 15 =
D. 11 + 18= 11 + 16= 11 + 17= 21 + 18 =
Digitized byCjOOQlC
GRADE III. THIRD SERIES 31
IV. PROBLEMS: AT SCHOOL
1. If in Harriet's schoolroom there are 22 boys and
21 girls, there are pupils present.
2. The room is divided into two classes. In one
class there are 10 boys and 11 girls. How many pupils
are there in this class?
3. How many are there in the second class, where
there are 10 girls and 12 boys?
4. One day in Harriet's room there are 32 pupils and
in Minnie's room 32 pupils. In both rooms there are
pupils. (In what two ways can you do this example?)
5. If this school has a 20-minute recess in the morn-
ing and a 15-minute recess in the afternoon, how many
minutes are given to recess during the day?
6. How long is the blackboard space in a room if
the front board is 33 feet long and the side board 32
feet long?
7. In Minnie's room there were 28 pupils present on
Monday and 11 pupils absent. What is the membership
of the school?
8. Jerry is asked to count the reading books for his
class. He finds two sets. One set has 25 books and
another set has 25 books. How many books does he
find ? (Do this in two ways.)
9. How much time is given to arithmetic in Harriet's
room if one class recites 12 minutes and the other 14
minutes ?
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82 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. Pupils should learn to recognize these differences at a glance.
The limit of numbers used is the same as in the three preceding exercises.
V. SUBTRACTION
A. 10 16 70 20 17 80 30 80 60
10 10 10 20 10 10 30 20 10
!. 70
50
11
90
11
25
12
15
12
10
10
11
10
10
25
12
10
10
VI. SUBTRACTION
A. 13 18 75 40 14 60 14 15 13
13
10
25
10
14
20
10
15
10
B. 50
30
30
35
40
50
20
40
19
20
10
20
35
20
50
10
40
10
C. 22
34
42
24
33
45
36
32
37
20
33
41
21
30
44
35
12
27
VII. SUBTRACTION
^.40-30= 50-30= 60-30= 70-30 =
B. 50 - 40 = 60 - 40 = 12 - 11 = 13 - 11 =
C. 21-11= 14-11= 22-11= 15-11 =
D. 18-11= 16-11= 17-11= 33-11 =
Digitized byCjOOQlC
GRADE III. THIRD SERIES 88
VIII. PROBLEMS: AT SCHOOL
1. If there are 40 children in Ehner's school and 20 of
these are boys, there must be girls.
2. How many pupUs are present in Elmer's school if
40 belong and 10 are absent?
3. When 11 children stay in at recess on a rainy day,
how many go out if 38 have come to school?
4. Elmer starts to school 35 minutes before it begins.
It takes him 25 minutes to go to school. How long does
he have to play before school begins?
5. If 40 children belong in Elmer's school and 45 belong
in Jenny's, there are more pupils in Jenny's school
than in Elmer's.
6. If in one class there are 15 boys and 11 girls, there
are more boys in the class than girls.
7. The teacher asks Sam to put 23 pieces of chalk
around the blackboards for the class to use. He can find
only 13 pieces in the box. How many more does he need ?
8. How much longer is the morning recess than that
in the afternoon if the afternoon recess is 15 minutes
long and the morning one is 20 minutes long?
9. The noon period is 90 minutes long. Susan can go
home, eat her dinner, and be back again in 60 minutes.
She has minutes to spare.
Additional Work. Each pupil should write out and bring to class
a similar problem of his oum.
Digitized by VjOOQ IC
34 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. Exercises to train pupils to think (without conscious reckoning)
the sum of two-figure numbers. No "carrying"; sums of units and of
tens less than 10. Pupils should think from left to right.
IX. ADDITION
.
A. 23
24
25
26 27 24
23
23
32
32
42
52
62 72 24
23
55
45
B.
32
32
33
33
33
34
34
34
35
57
63
44
55
66
53
23
44
63
X. ADDITION
A.
35
45
45
45
46
46
46
47
47
42
22
33
44
33
22
53
12
42
B.
47
48
52
53
54
55
55
56
56
52
31
25
35
45
22
44
23
33
C.
42
32
53
35
33
75
13
18
35
37
43
24
62
45
24
65
41
44
XI. ADDITION
A. 56 + 33= 62 + 35= 63 + 36= 64 + 24 =
B. 65 + 34= 66 + 22= 66 + 33= 72 + 23 =
a 72 + 24= 81 + 18= 72 + 25= 72 + 17 =
2>. 72 + 27= 55 + 14= 77 + 22= 52 + 33 =
Digitized byCjOOQlC
GEADE III. THIRD SERIES 36
XII. PROBLEMS: AT SCHOOL
1. In a certain school there were 45 readers of one
kind and 44 readers of another kind. How many readers
were there of the two kinds?
2. In a two-room building 72 children were present
and 16 were absent. There must have belonged in the
two rooms children.
3. How many pupils belonged in a school where 23
were girls and 31 were boys?
4. On a rainy day the teacher counted 17 pupils who
did not go out at recess. There were 22 on the play-
ground. How many were present that day?
5. If at the close of the school year 66 arithmetics
were put away in the storeroom and 23 were sent away
to be repaired, there must have been arithmetics in
the school at the close of the year.
6. How many desks are there in a room where there
are 22 on one side and 22 on the other side? (Think
this problem in two ways.)
7. A sheet of paper is to be passed to each of the pupils
in a class of 24 and a sheet to each in a class of 23. How
many sheets must be counted out for both classes ?
8. The teacher has 43 sheets and sends to the prin-
cipal for 15 sheets more. Is that enough to give a
sheet to each one in a class of 48 pupils?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
Digitized byCjOOQlC
36 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. Exercises to train pupils to think the differences of two-figure
numbers. No " borrowing " is required ; therefore the differences should be
thought from left to right as one reads.
XIII. SUBTRACTION
A. 41 49 42 48 59 51 58 52 45
20 19 31 24 42 20 16 31 23
70
57
46
49
47
62
53
52
63
30
35
11
23
24
31
43
22
23
XIV. SUBTRACTION
A. 55 64 65 56 66 72 73 67 68
30 44 60 24 33 40 31 24 34
B. 80
74
79
75
89
76
82
99
77
40
22
45
25
41
46
82
22
11
C. 88
99
66
55
77
87
78
99
88
55
25
43
22
77
77
77
66
34
XV. SUBTRACTION
A. 75-35= 78-54= 88-44= 83-30 =
5. 84-42= - 85-24= 91-50= 98-44 =
C. 92-41= 86-35= 93-33= 97-65 =
B. 87-52= 94-22= 95-15= 96-72 =
Digitized byCjOOQlC
GRADE III. THIRD SERIES 37
XVI. PROBLEMS: AT SCHOOL
1. Of a pile of 95 paper pads 35 were distributed to the
pupils. How many pads remained in the pile ?
2. If a school of 42 pupils uses 1 pad of white paper
and 84 pads of yellow scratch paper a month, they use
more yellow than white pads.
3. It requires 37 rubber erasers to supply one to each
pupil in a school. The teacher finds she has only 22 erasers.
How many more does she need for her school ?
4. In Jerry's reading class of 25 children there are not
enough books to go around. If 13 children listen while
the others read, how many books are there?
5. Hester is in a class of 23 pupils. The teacher asked
her to take enough arithmetics from a pile of 37 so that
each of her class could have one. There are two ways
for her to solve her problem. Which is the easier way?
6. Four packages of pencils contain 48 pencils. John is
asked to take enough pencils to supply one to each of his
class of 38 pupils. John can proceed in two ways. Which
is the easier ?
7. At the end of the year the teacher finds that of the
45 desks in her room 13 have been so badly scratched that
they must be repaired. How many careful pupils were there
in the school ?
Additional Work. Each pupil shovid write out and bring to class
a similar problem of his otm.
Digitized byCjOOQlC
38 PRA.CTICE EXERCISES IN MENTAL ARITHMETIC
Note. These are reciew exercises in multiplication. Pupils should
recognize products at a glance.
XVII. MULTIPLICATION
A.
1
10
44 12
25 32
23
33
50
1
1
2 3
1 2
2
J
2
B.
70
34
20 30
21 32
21
11
25
1
2
3 2
3 3
4
4
4
XVIII. MULTIPLICATION
A.
12
11
22 12
9 11
8
12
7
_i
_5
A A
_6 J_
9
6
8
B.
10
12
8 7
5 3
6
11
6
9
8
8 9
8 9
8
6
7
a
9
9
8 8
9 9
7
5
4
12
8
7 12
9 7
12
9
9
XIX. MULTIPLICATION
A.
6x
6 =
12x7 =
4x9 =
9x9 =
B.
9x
11 =
5x9 =
8x4 =
7x5 =
c.
8x
3 =
7x7 =
7x4 =
9x1 =
D.
20)
<2 =
30x3 =
22x3 =
33 X 2 =
E.
44)
<1 =
18x1 =
60x1 =
20x5 =
Digitized by Google
^.
1
GRADE III. THIRD SERIES 39
XX. PROBLEMS: AT SCHOOL
1. If there are 25 pupils in your class and each pupil
uses 3 pads of paper in a term, it will take pads
to supply the class.
2. The teacher gives a box of 8 colored crayons to
each child in a class of 12 children. How many crayons
were there altogether?
3. If 30 sheets of paper were cut into 3 pieces each, it
would be enough to supply pupils with one piece each.
4. There are 2 rooms in Jacob's schoolhouse. If in
each room there are 42 desks, there must be desks
in the two rooms. (Think this in two ways.)
5. A janitor collects 8 bushels of waste paper each day.
He will then collect bushels in a school week.
6. Elizabeth is in a class of 23 children. They use
3 different reading books in one term. The teacher will
ne6d to order readers for that class for the term.
7. During the year in one room in a building 20
packages of composition paper are used. How many
packages must be supphed to a 5-room building if each
room uses the same amount?
8. If there are 22 books in each of 4 sets, how many
covers are needed if each book is to be covered?
9. At the close of the year in one school 9 books were
found to be worn out in each of 6 different sets of readers.
Then new books should be bought for those sets.
Digitized by VjOOQIC
40 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. These are review exercises in division. Pupils should recognize
the quotients at a glance.
XXI. DIVISION
A. ijl 1)2 1)3 iJIO 2)18 2)22
B. 3)30 2)24 3)36 3j60 3)39 3)66
a 3)90 3)63 3)93 3)69 4)16 4)i0
XXII. DIVISION
A. 4)20 4)44 4)48 5)30 5)40 5)55
5. 6)18 6)36 7)21 7)35 6)24 6)66
C. 7)28 6)42 7)49 6)72 7)56 8)24
^. 84 + 7 =
32 H- 8 =
/x V x«xv>rxi
27 + 9 =
48 + 8 =
5. 36+9 =
63 + 9 =
96 + 8 =
80+8 =
C. 99 + 9 =
54 + 9 =
81+9 =
64 + 8 =
2). 45-*-9 =
72 -.-8 =
25 + 1 =
99 + 3 =
.E. 77 H- 7 =
77 + 1 =
20+1 =
75 + 3 =
Digitized by Google
GRADE III. THIRD SERIES 41
XXIV. PROBLEMS: AT SCHOOL
1. The principal of a school has ordered 48 erasers
for use at the blackboard. If these are divided equally
among 4 rooms, each room will receive erasers.
• 2. If there were 8 rooms among which the 48 erasers
were to be equally distributed; how many would each
room receive?
3. There are 42 desks to be put mto a schoolroom. If
they are arranged in 6 rows, in each row there will
be desks.
4. There are 3 classes in a school to be supplied with
reading books, and 60 books are ordered. If the same
nmnber of books is given to each class, each will receive
books.
5. There are 36 children in a school. The teacher
separates them into 6 equal groups. How many children
are in each group?
6. In a school of 44 pupils there are two classes of
equal size. If one class is dismissed pupils remain
at their seats.
7. The teacher gives the class in arithmetic slips of
paper 9 inches long. She says, '^Divide your slips into
3 equal parts." How long will each part be?
8. If the 9-inch strips were divided into 9 equal parts,
each part would be inch long.
Additional Work. Each pupil should write out and bring to class
a similar problem of his otvn.
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40 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. These are review exercises in division. Pupils should recognize
the quotients at a glance.
XXI. DIVISION
A, 1)1 1)2 1)3 l)IO 2)18 2)22
B. 3J3O 2)24 3)36 3)60 3)39 3)66
c. 3)90
3)63 3)93
3)69
4)16
4)40
XXII. DIVISION
^. 4)20
4)44 4)48
5)30
5)40
5)55
B. 6)18
6)36 7)21
7)35
6)24
6)66
C. 7)28
6)42 7)49
6)72
7)56
8)24
XXra. DIVISION
^.84 + 7-
s-> ^ s =
27 H- 9 =
48 + 8 =
B. 36+9-
IW ^ 1» =
iW-^B-*
^80fS= ,
a 99 -•- i> =
64 * 9 =
?!-
Ig4^
S^
Z). 45+9-
T-i -^ S -
%M
u
F
J. 77+7 =
t: + 1 «
^
■
iGbogk
1^
4t
^5ui,z ILL TH:s:t, xr,;c(zji
X, "^
a?^
L'X IfOLi. aTfL ii
• v.* .'
>.• •£.<
^ ^Ji^f?^ S?- ^«
n
M i>
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42 PRACTICE EXERCISES m MENTAL ARITHMETIC
XXV. PROBLEMS: MISCELLANEOUS
1. If a school day is 5 hours long, how many hours are
there in a school week ?
2. In some schools there are 30 hours in a school week.
In these schools a school day is hours long.
3. When schools keep 20 days each school month, at
the end of a term of 3 months the schools have kept
days.
4. Harry was out of school sick for 20 days during a
period of 80 school days. How many days did he attend
school during that time?
5. Judith is planning her school garden. She has a
strip of ground 18 feet long. How many '' hills " can she
plant in a row if she plants them 3 feet apart ?
6. If Judith plants her hills 2 feet apart she will have
9 hills. How many seeds will she need if she puts 4 seeds
in each hill ?
7. Joe planted tomatoes in his school garden. He has
6 vines and picks 6 good tomatoes from each vine. His
crop of good fruit is then . tomatoes.
8. Jerry picks 45 good tomatoes from his vines. He
sells 25 of them to a neighbor and gives the rest, or
tomatoes, to his mother.
9. In a two-room school there are 40 boys and 35 girls.
How many pupils belong to this school?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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GRADE III. THIRD SERIES 43
XXVI. PROBLEMS: MISCELLANEOUS
1. Ethel's class in school is given, 3 times a week, 5
words to learn to spell. At the end of the week the class
has studied words.
2. At the end of a school month of 4 weeks Ethel's
class in spelling has studied 60 words. Of these, 20 words
did not need very hard study, for Ethel knew them pretty
well already. How many hard words were there to be
studied ?
3. There are 26 letters in the alphabet. Henry can write
the capital form of 22 of them. He is uncertain about
capital forms.
4. On page 40 there are 56 examples. If you make a
mistake in 16 of them, how many can you do correctly?
5. If by 4 minutes' study you have mastered the 16
difficult examples, how many have you mastered each
minute ?
6. There are three ways in which you can find out the
number of examples in Exercise XXIII, page 40. What
are the three ways and which is the best ?
7. When you take 20 minutes to learn a lesson that you
can learn in 15 minutes, how much time have you wasted ?
8. If you can give the correct answer to each of the
examples in Exercise XXIII, page 40, in 3 seconds, how
long will it take you to do the entire exercise ?
Additional Work. Every pupil should write out and bring to class
a similar problem of his own.
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GRADE III. FOURTH SERIES
Note. The Fourth Series consists of exercises in using combinations
that should now be familiar, but they appear here under the mask of
United States money symbols.
I. ADDITION
A. $0.03 $0.04 $0.02 $0.05 $0.08 $0.09
.03 .04 .02 .05 .02 .01
£.
$0.05
.02
$0.04
.01
$0.05
.01
$0.09
.02
$0.04
.02
$0.01
.01
II. ADDITION
A.
$0.06
.01
$0.03
.02
$0.04
.03
$0.03
.01
$0.08
.01
$0.06
.02
B.
$0.07
.01
$0.06
.03
$0.05
.04
$0.06
.06
$0.07
.07
$0.02
.01
III. ADDITION
A.
$0.07
.02
$0.05
.03
$0.09
.09
$0.01
.03
$0.01
.08
$0.02
.06
B.
$0.01
.07
$0.03
.06
$0.04
.05
$0.01
.02
. $0.02
.07
$0.03
.05
a
$0.06
.06
$0.07
.07
$0.09
.09
$0.01
.03
$0.03
.04
$0.02
.03
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GRADE III. FOURTH SERIES 45
IV. PROBLEMS: EARNING, SAVING, AND SPENDING
1. If Ralph puts into his bank $0.05 of the money
he received for doing errands, and the rest, amounting
to $0.03, he spends for candy, he must have earned
doing errands.
2. Ralph's little brother Tim helped him shovel snow
from the sidewalk, and for this Ralph gives him at one
time $0.01 and at another time $0.02. How much does
little Tim earn in this way?
3. Joan is paid $0.02 at two diflEerent times for doing
errands for the neighbors. For these two errands she
receives . (In what two ways can you do this
problem. Is one way easier?)
4. When Ralph has spent $0.05 for a ticket to a
moving-picture show and $0.02 for gum, how much
money has he spent?
5. Francis decides to put $0.09 aside in his Christmas-
present fund. This is half of what he earned during
the week. How much did he earn? (Do this problem
in two ways.) s
6. Ralph and Francis go to the drug store. Francis
spends $0.05 for an ice-cream cone and Ralph spends
the same amoimt for a soda. The clerk received from
both boys . (Do this in two ways.)
7. How much money has Joan after she has foimd a
nickel if she already had $0.03 in her pocketbook?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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46 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. The following are exercises in recognizing the more difl&cult
addition combinations under the mask of United States money symbols.
V. ADDITION
A. $0.07 $0.09 $0.07 $0.08 $0.08 $0.07
.05 .05 .03 .04 .08 .04
B.
$0.09
.03
$0.08
.03
$0.06
.04
$0.06
.05
$0.07
.06
$0.09
.06
VI. ADDITION
A.
$0.09
.08
$0.09
.04
$0.08
.06
$0.08
.05
$0.08
.07
$0.09
.07
B.
$0.04
.07
$0.08
.08
$0.04
.08
$0.03
.07
$0.05
.09
$0.05
.07
C.
$0.03
.09
$0.05
.06
$0.03
.08
$0.06
.07
$0.04
.06
$0.06
.09
VII. ADDITION
A. $0.05 + .08 = $0.07 + .09 = $0.07 + .08 =
B. $0.06 + .08 = $0.08 + .09 = $0.09 + .05 =
C. $0.09 + .04 = $0.07 + .05 = $0.08 + .06 =
D. $0.08 + .07 = $0.09 + .06 = $0.09 + .07 =
Digitized byCjOOQlC
GRADE III. FOURTH SERIES 47
VIII. PROBLEMS: EARNING, SAVING, AND SPENDING
1. When Lois has saved $0.09 and has received $0.08
as a gift, she has that she can put in the bank.
2. Frank has $0.08 and he earns $0.08 raking leaves
from the yard. How much has he that he can use towards
the purchase of a bat ? (Do this in two ways.)
3. Frank and Arthur want to start a play store. Frank
can put into the partnership $0.05 and Arthur can put in
$0.07. Together they have with which to buy things
for their store.
4. If Lois spends $0.04 for cookies for her doll's party
and $0.06 for fruit, how much does her party cost?
5. How much does Lois earn all day Saturday if her
mother gives her $0.06 for helping her in the morning,
and in the afternoon a neighbor gives her $0.07 for taking
the baby for a ride in the baby carriage ?
6. Arthur's father agrees to give him $0.07 a week to
keep his mother supplied with coal for the kitchen stove.
How much does he receive at the end of two weeks ? (Do
this in two ways. Which way do you prefer ?)
7. On the first day of December Frank and Lois begin to
think of Christmas. Frank counts his money. It amounts
to $0.09. Lois counts hers and says that she has $0.07.
How much do they have together with which to buy
Christmas presents?
Additional Work. Each pupil shoidd write out and bring to class
a similar problem of his own.
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48 PRACTICE EXERCISES m MENTAL ARITHMETIC
Note. The following are exercises in recognizing dUSerences of what
should now be familiar combinations, but under the mask of United States
money symbols.
IX. SUBTRACTION
A. $0.09 $0.01 $0.04 $0.08 $0.05 $0.09
.01 .01 .02 .02 .05 .02
B. $0.05 $0.06 $0.08 $0.03 $0.04 $0.06
.01 .02 .01 .01 .03 .01
X. SUBTRACTION
A. $0.03
.02
$0.04
.01
$0.05
.02
$0.08
.03
$0.09
.05
$0.07
.02
B. $0.07
.05
$0.09
.05
$0.07
.03
$0.08
.04
$0.08
.08
$0.07
.04
a $0.09
.09
$0.03
.01
$0.06
.04
$0.05
.03
$0.06
.03
$0.06
.06
XL SUBTRACTION
A. $0.09 - .03 = $0.08 - .03 = $0.06 - .04 =
B. $0.07 - .06 = $0.09 - .04 = $0.09 - .08 =
a $0.09 -.07= $0.08 -.07= $0.08 -.05 =
D. $0.09 -.05= $0.07 -.05= $0.03 -.03 =
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GRADE III. FOURTH SERIES 49
XIL PROBLEMS: EARNING, SAVING, AND SPENDING^
1. Jerry earns $0.10 and spends $0.09. He has
left.
2. If Rosa has $0.08 in the bank and takes out $0.08,
how many cents has she left in the bank?
3. How much money does Joe have when he reaches
the store if his mother gives him $0.07 and he loses
$0.02 on the way?
4. Joe reaches the store with $0.05 and buys a yeast
cake for $0.03. The storekeeper should give him
in change.
5. When Jerry has saved $0.08 he decides to put
$0.05 in his bank. He has then left to spend.
6. Jerry and Joe have $0.07 each. How much more
does Jerry have than Joe?
7. Rosa goes to a candy shop. She can buy 3 candy
balls for a cent or 2 chocolate creams for a cent.
Which kind can she buy more of for a cent, and how
many more?
8. Joe can buy a pair of shoe strings for $0.05 or
two pairs for $0.09. How much will he save by buy-
ing two pairs at one time? (You can do a part of this
in two ways. Which is the better way?)
Additional Work. Hack pupil should write out and bring to class
a similar problem of his own.
Digitized byCjOOQlC
60' PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. The following are exercises in thinking the products of what
should be familiar combinations, but under the mask of United States
money symbols. They contain the thirty-six combinations of numbers to
12 X 9 (out of a possible seventy-two) that give the least difficulty.
XIII. MULTIPLICATION
A.
$0.10
1
$0.08
2
$0.02
2
$0.02
1
$0.05
1
$0.12
1
B.
$0.06
1
$0.07
1
$0.03
2
$0.09
1
$0.03
3
$0.05
2
XIV.
MULTIPLICATION
A.
$0.03
1
$0.04
1
$0.11
1
$0.10
2
$0.10
4
$0.04
2
B.
$0.05
5
$0.07
2
$0.10
3
$0.09
2
$0.01
1
$0.11
2
C.
$0.05
3
$0.06
2
$0.05
4
$0.08
2
$0.10
5
$0.07
3
XV. MULTIPLICATION
^.$0.04x3= $0.04x4= $0.10x6= $0.12x2 =
B. $0.10x8= $0.10x7= $0.03x5= $0.02x6 =
C. $0.04x5= $0.02x8= $0.03x7= $0.03x4 =
D. $0.02x12= $0.02x11= $0.02x9= $0.02x7 =
Digitized by VjOOQIC
GRADE III. FOURTH SERIES 51
XVI. PROBLEMS : EARNING, SAVING, AND SPENDING
1. Ned earns $0.25 on Monday and $0.25 on Tuesday ;
how much has he earned by Tuesday night? (Do this in
two ways. Which way do you prefer ?)
2. Ned has $0.04 and his sister Lucy has four times as
much. Then Lucy has .
3. Joseph charges $0.10 for cleaning snow from ^
sidewalk. If he cleans 5 sidewalks during one snow-
storm, how much does he earn? (Do this in two ways
and tell which is the easier way.)
4. Jenny has $0.08 in her bank and Mary, her older
sister, has eight times as much. How much has Mary?
(Do this in two ways. Which is the better way?)
5. Ned goes to the store to buy Christmas cards. He
selects those that sell for $0.03 each. He buys 7 of them
and pays .
6. Lucy buys 4 cards that cost $0.05 each. How much
does she pay ?
7. If Jenny earns $0.12 a week, how much will she earn
in a fortnight ?
8. Little Tom helps his big brother sell newspapers.
A profit of $0.01 is made on each paper. When Tom has
sold 12 papers he has made .
Additional Work. Each pupil should write out and bring to class
a similar problem of his oum.
Digitized byCjOOQlC
62 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. The following are the products of the more difficult combination^
of numbers to 12 x 9 arranged in the probable order of progressive difficulty.
XVII. MULTIPLICATION
A
$0.10
9
$0.11
3
$0.06
3
$0.11
5
$0.06
6
$0.11
4
B.
$0.06
4
$0.08
5
$0.11
7
$0.06
5
$0.11
6
$0.08
3
XVIII
. MULTIPLICATiON
A.
$0.11
8
$0.09
5
$0.09
3
$0.07
5
$0.11
9
$0.12
3
B.
$0.07
4
$0.08
4
$0.12
4
$0.09
9
$0.07
7
$0.12
5
a
$0.07
6
$0.09
4
$0.08
6
$0.12
6
$0.08
8
$0.09
6
XIX. MULTIPLICATION
A. $0.12x9= $0.09x8= $0.08x7= $0.12x7 =
B. $0.09x7= $0.12x8= $0.06x8= $0.06x12 =
C. $0.04x9= $0.06x9= $0.09x12*= $0.08x9 =
D. $0.07x8= $0.07x12= $0.07x9= $0.08x12 =
E. $0.25x4= $0.25x3= $0.25x2= $0.50x2 =
Digitized byCjOOQlC
GRADE III. FOURTH SERIES 53
XX. PROBLEMS: EARNING, SAVING, AND SPENDING
1. When Sam has sold 9 heads of lettuce from his
garden for $0.05 a head, he has earned .
2. When radishes are selling in the market for $0.03
a bmich, Julius will save for his mother if he
gives her 9 bunches out of his garden.
3. Harriet works 4 hours one week in her garden. If
her time is worth $0.08 an hour, what is the value of the
time she has put into garden work diu'ing the week ?
4. Sam is paid $0.12 for pulling 100 weeds out of
the lawn. How much will be due him when he has
pulled 800 weeds? (Is this too much or too little for
pulling weeds?)
5. Julius prefers to work by the hour and is paid at
the rate of $0.11. After he has worked 9 hours he
has earned .
6. Sam puts in his bank $0.06 out of every $0.12
he earns. After he has pulled 800 weeds he should put
in his bank.
7. From what he earns each horn- Julius takes $0.06
to put away for Christmas presents. How much has he
put aside after he has received pay for 9 hours' work?
8. At Christmas time Harriet wishes to spend $0.25
on a present for each of her 3 friends. How much
money will she need?
Additional Work. Each pupil sJumld write out and bring to class
a similar problem of his own.
Digitized byCjOOQlC
64 PRACTICE EXERCISES IN MENTAL ARITHMETIC
Note. The following are exercises in thinking the quotients of what
should now be familiar combinations, bat under the mask of United States
money symbols. The products in Exercises XVII-XIX are here used as
dividends.
XXI. DIVISION
A. 9)$0.90 3)$0.33 3)$0.18 5)$0.55 6) $0.36
B. 4)$(X44 4)$0^ 5)$0.40 7)$(X77 5j$0J0
a 6)$0^ 3)1024 SJWSS 5j|0l5 3j|a27
XXII. DIVISION
^. 5)$0.35 9)10.99 3)$0.36 4)$0.28 4)$0.32
B. 4)$0.48 9)$0.81 7)$0.49 5)$0.60 6)$0.42
a 4)$0J6 6j$08 6)$0J2 8) $0.64 6)$0M
XXIII. DIVISION
A $1.08 -«- 9= $0.72 + 8= $0.56 +7= $0f84-s-7 =
B. $0.63-*- 7= $0.96+8= $0.48 -i- 8= $0.72+12 =
a $0.36 + 9= $0.54 + 9= $1.08 + 12= $0.72 + 9 =
D. $0.56 + 8= $0.84+12= $0.63 + 9= $0.96 + 12 =
E. $1.00 + 4= $0.75 + 3= $0.50 + 2= $1.00 + 2 =
Digitized byCjOOQlC
GRADE III. FOURTH SERIES 56
XXIV. PROBLEMS: EARNING, SAVING, AND SPENDING
1. Sam receives $0.45 for 9 heads of lettuce that he
sells from his garden. How much does he receive for
each head?
2. Paul's mother would pay $0.27 for 9 bunches of
radishes if she bought them at the store. If Paul sells
those he' raises in his garden at the same rate, he will
charge a bunch.
3. Harriet thinks that when she has worked 4 hours
in her garden she has put in work to the value of $0.32.
This is at the rate of an hour. (Does Harriet esti-
mate her work at too high a value ?)
4. Paul is paid $0.99 for 9 hours' work. How much
does he receive an hour ? (Is this good pay for a ten-year-
old boy?)
5. From the money Sam receives for pulling weeds he
puts in his bank $0.48. He earns this money by pulling
800 weeds. How much does he earn for his bank by
pulHng 100 weeds?
6. Paul has a Christmas fund of $0.54. He has taken
it from the money he earned by working 9 hours. How
much did he earn each horn- for his Christmas fund ?
7. At Christmas time Harriet spends $0.75 for presents
for her 3 friends. She pays the same for each present.
Then she spends for each friend.
Additional Work. Each pupil sTioiUd write out and bring to class
a similar problem of his otvn.
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56 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XXV. PROBLEMS: MISCELLANEOUS
1. Uncle Reuben has a cherry tree. He tells John,
Harry, and Ralph that he will give them $0.03 a quart
to pick the cherries. John picks 10 quarts, Harry 12
quarts, and Ralph 8 quarts. How much does Uncle Reuben
pay each boy ?
2. Uncle Reuben sells 9 quarts of cherries for $0.81.
What is the price for a quart?
3. If the cherries cost $0.03 a quart to pick and they
are sold for $0.09, Uncle Reuben makes a profit of
on each quart that he sells.
4. Uncle Reuben has a pear tree also. He agrees to pay
the boys $0.11 a bushel to pick the pears. How much
should Ralph receive for picking 4 bushels ? (Which is the
easier of the two possible ways of doing this ?)
5. If Harry works 6 hours picking pears and receives
$0.66, how many pears did he pick during that time?
6. Harry earns $0.09 while John is earning $0.07.
Then he earns more than John does in the same
time.
7. If Harry earns $0.03 more than John does in an
hour, he will be worth more than John at the end
of 5 hours.
Additional Work. Each pupil %hovld write out and bring to class
a similar problem of his own.
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GRADE HI. FOURTH SERIES 57
XX VI. PROBLEMS: MISCELLANEOUS
1. Eleanor, Bessie, and Hester have the same amount
of money. They put it all in a pile and find that they
have together $0.30. Then each one must have had .
2. Eleanor spends $0.06 of her $0.10 and has left.
3. Bessie loses $0.01 of her $0.10 and puts the rest in
the bank. How much does she put in the bank ?
4. Hester buys a ticket to the " movies " for $0.05. Of
her $0.10 she has left.
5. One day in the autumn the three girls with two of
their friends rake the leaves from the lawn and receive
$0.05 each from Hester's mother for doing it. Hester's
mother paid for having the leaves raked from
the lawn.
6. Eleanor earned that same week $0.03 for going on
an errand and $0.09 for helping mother with the dishes.
At the end of the week how much did she have to add
to the $0.05 earned in raking leaves?
7. Bessie is given $0.02 a day if she is careful to throw
the bedclothes over the foot of her bed every morning. If
she remembers this every day, in 9 days she can earn .
8. Ned and 4 of his friends form a saving club.
Each promises to save $0.07 a week. If the boys keep
their promise, how much will they together save in
a week?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
Digitized byCjOOQlC
TO TEACHERS
Before beginning the work of the fourth grade it will be well to
make sure that the pupils are proficient in the third-grade work.
It would not be amiss to go rapidly through all the abstract exer-
cises with those classes that have not studied them. At least the
Third and Fourth Series should be reviewed.
If a review as extensive as that suggested is not desired, have
pupils practice the combinations on pages 46, 52, and 54, for these
are the combinations that give the most trouble.
58
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TABLES OP MEASURES
Note. Only those items are included in the following tables that pupils
of fourth-grade age are accustomed to meet in their out-of-school life.
MEASURES OF LENGTH
12 inches (in.) = 1 foot (ft.)
3 feet (ft.) = 1 yard (yd.)
MEASURES OF SURFACE OR AREA
144 square inches (sq. in.) = 1 square foot (sq. ft.)
9 square feet (sq. ft.) = 1 square yard (sq. yd.)
MEASURES OF SOLIDS
1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.)
27 cubic feet (cu. ft.) = 1 cubic yard (cu. yd.)
MEASURES OF LIQUIDS
4 gills (gi.) = 1 pint (pt.)
2 pints (pt.) = 1 quart (qt.)
4 quarts (qt.) = 1 gallon (gal.)
MEASURES OF TIME
60 seconds (sec.)
60 minutes (min.)
24 hours (hr.)
7 days (da.)
365 days (da.)
52 weeks (wk.)
12 months (mo.)
= 1 minute (min;)
= 1 hour (hr.)
= 1 day (da.)
= 1 week (wk.)
= 1 year (yr.)
= 1 year (yr.)
= 1 year (yr.)
MEASURES OF PAPER
24 sheets = 1 quire
500 sheets = 1 ream
59
MEASURES OF DRY SUB-
STANCES
2 pints (pt.) = 1 quart (qt.)
8 quarts (qt.) = 1 peck (pk.)
4 pecks (pk.) = 1 bushel (bu.)
MEASURES OF UNITED
STATES MONEY
10 mills =lcent(#orct.)
10 cents = 1 dime (d.)
10 dimes = 1 dollar ($)
100 cents = 1 dollar
COUNTING
12 units = 1 dozen (doz.)
144 units = 1 gross (gro.)
12 dozen = 1 gross (gro.)
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GRADE IV. FIRST SERIES
I. READING NUMBERS
Note. Pupils should not use the word and in reading whole numbers.
242 should be read "two hundred forty-two"; 301 should be read "three
hundred one."
A. 113
222
345
401 510
635
808
B. 950
708
872
II.
698 384
ADDITION
999
650
Note. As in previous exercises pupils should see the sums without
conscious calculation.
A. 1
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1
2 2
2
3
4
5
6
7
8
2 3
B. 1
1
1
1
2
2
2
2 2
2
2
2
2
2
2
2
2 2
4
5
6
7
2
3
4
5 6
III.
ADDITION
A. 3
3
3
3
3
3
3
4 4
2
2
2
3
3
3
1
4 4
3
4
5
1
3
4
5
1 2
B. 4
2
1
1
5
3
1
2 4
1
6
8
7
3
4
7
6 3
5
2
1
2
2
3
1
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1 2
Google
GRADE IV. FIRST SERIES 61
IV. PROBLEMS: AT HOME
1. John lives at 205 Edgewood Avenue, Mary at 444
South Street, and Harry at 520 Stanley Road. (Be sure
that you can read these numbers correctly.)
2. Harold lives on a farm. In April his father put
into the chicken incubator 912 eggs. In three weeks
887 chickens were hatched. Read the numbers correctly.
3. Sarah lives in the country. She goes 2 miles to
school, 3 miles farther to the village, and 1 mile beyond
the village to the railroad station. The station is
miles from Sarah's home.
4. Mother sends Edith to the store to buy Christmas
presents. How many dolls does she buy if she buys 2
for her little sister, 2 for her cousin Lottie, and 4 for
the neighbors' children?
5. Frank coimts up the number of children whom he
wishes to invite to his party. There are 3 boy friends
and 3 girl friends besides his 2 sisters. How many does
he invite?
6. How many quart jars of preserves does Julia's
mother make if she puts up 7 jars of peaches, 2 jars
of pears, and 1 jar of plums?
7. Julia goes to her aunt's home to make a visit. It
takes a day to go, she spends 5 days there, and it takes
a day to return. Then Julia spends days away
from home.
Additional Work. Each pipil should vnrite out and bring to class
a similar problem of his ovm.
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62 PRACTICE EXERCISES IN MENTAL ARITHMETIC
V. READING NUMBERS
^. I n in IV V VI VII viii
B. IX X XI XXII XXXIII XL XLI XLV
C. XL VI XLIX L XIV XVI XXVII XXXVIII
VI. ADDITION
Note. Train pupils to see at a glance the two numbers that in sequence
make 10 and then add the third number. The skill gained in this practice
should be carried over into all column and line addition.
A. 1
1
2
2
3
O
4
4
5
1
2
3
4
5
6
7
8
9
9
8
7
6
5
4
3
2
1
B. 5
4
2
3
1
8
6
9
7
5
6
8
7
9
. 2
4
I
3
1
4
5
1
6
7
8
4
6
VII. ADDITION
A. 1 + 9 + 1= 2 + 8 + 3= 4 + 7 + 3= 5 + 5 + 5 =
B. 4 + 6 + 7= 8 + 4 + 6= 7 + 6 + 4= 9 + 1 + 5 =
C. 7 + 1 + 9= 9 + 8 + 2= 8 + 3 + 7= 7 + 3 + 9 =
D. 6 + 7 + 3= 4 + 9 + 1= 8 + 2 + 5= 7 + 2 + 8 =
E. 1 + 9 + 8= 7 + 3 + 7= 4 + 6 + 4= 2 + 8 + 2 =
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GEADE IV. FIRST SERIES 63
VIIL PROBLEMS: AT HOME
1. Lilian and Joseph were playing school. Lilian was
teaching Joseph to make Roman numbers. Here are some
questions she asked him. Answer them if you can.
a. How do you make the Roman number ^ve?
&. What do you do to the Roman five to make the
Roman four ?
c. What do you do to the Roman five to make the
Roman sir?
d. How do you make the Roman teii ?
6. Change the Roman ten to the Roman nine ; change
it to the Roman eleven.
2. Have pupils ask each other similar questions about
Roman numbers.
3. Joseph has a hen that hatched only 2 chicks from
a dozen eggs. Joseph gave her 3 other chicks that had
strayed from their mother, and 7 whose mother a hawk
had carried off. This made chicks for the mother hen.
4. Lilian collected 6 eggs from one nest, 4 from another
nest, and 8 from a third nest. How many eggs did she
find?
5. There are three parts to the driveway from the street
to the garage at Joseph's house. From the curbstone to
the front fence is 4 feet. From the fence to the comer of
the house is 6 feet. From the comer of the house to the
garage is 7 feet. Then the driveway is feet long.
Additional Work. Each pupil should vrrite out and bring to class
a similar problem of his own.
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64 PRACTICE EXERCISES IN MENTAL ARITHMETIC
IX. COUNTING
A. Count by 2's to 100. C. Count by 4's to 100.
B. Count by 3's to 99. J). Count by 5'8 to 100.
X. SUBTRACTION
Note. Before taking this exercise review pages 20 and 22.
A 5 15 15 25 25 7 17
2 _2 12 _2 22 3 13
B. 37 57 9 19 19 49 7
23 43 2 _2 12 22 4
C. 17 57 8 18 28 58 58
4 54 § _§ 13 13 M
B. 9 19 19 39 17 27 57
5 _5 15 35 ^ 7 7
XL SUBTRACTION
A. 17-10= 18-13= 28-13= 28-23 =
B. 48-43= 50-30= 75-25= 60-40 =
C. 52-22= 33-11= 66-22= 55-33 =
D. 77-22= 44-11= 50-25= 50-20 =
^.41-11= 51-11= 57-7= 57-57 =
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GRADE IV. FIRST SERIES 66
XII. PROBLEMS: AT HOME
1. Fred's mother had a basket of eggs from which she
wished to sell 5 dozen. She asked Fred to count them out
by 2's. Coimt them for Fred. Fred thought he could count
them out more quickly by 3's. Why would he not count
them out by 4's or 5's ? Could he easily count them out
by 6's?
2. From a bag containing 20 pounds of flour Fred's
mother takes enough to do the Saturday baking. On
weighing the bag later it is found to contain 14 pounds,
so his mother must have used pounds.
3. Mother asks Jenny to polish the knives, forks, and
spoons. Of the knives there are 24, but 2 are kitchen
knives that do not need polishing. That leaves
knives to be polished.
4. When Jenny has polished 12 knives there are
knives left, but only knives remain to be polished.
5. If there are 23 forks in all and 10 of them are steel
while the rest are silver, how many are silver ?
6. There are 48 spoons — some teaspoons and some table-
spoons. Jenny picks out the tablespoons and finds that
there are 14 of them. How many teaspoons are there?
7. There are in all 93 articles to be polished. Jenny
works an hour, and then there are still 50 articles to polish.
She had polished articles in the hour.
Additional Work. JEach pupil should write out and bring to class
a similar problem of his own.
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66 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XIII. READING NUMBERS
Note. When reading dollars and cents the word and should be used at
the period only, f 101.10 is read "one hundred one dollars and ten cents."
A. $1.10
$1.01
$3.00
$5.50
$6.25
B. $0.16
$0.04
$0.35
$9.15
$7.05
C. $8.80
$3.20
$4.44
$9.99
$0.90
XIV. MULTIPLICATION
Note. Have pupils give the products as rapidly as they read a page of
easy prose. Additional practice may be given by reversing the order of the
numbers.
A. 12
9
8
12
9
9
12
12
12
_9
8
7
_8
9
7
11
10
7
B. 8
9
9
11
9
8
12
7
12
8
5
4
10
6
4
12
7
_6
C. 12
8
7
6
8
11
7
11
8
5
6
6
6
5
_6
4
11
3
XV. MULTIPLICATION
A 7x3= 12x4= 6x5= 11x7 =
Al2x3= 9x3= 11x8= 6x4 =
C. 8x2= 11x9= 11x3= 6x3 =
D. 6x2= 10x6= 12x2= 9x2 =
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GRADE IV. FIRST SERIES 67
XVI. PROBLEMS: AT HOME
1. If Jerry sleeps 9 hours every night for 5 nights,
he will sleep hours in that time. How many hours
will he sleep in 10 nights ? (In what two ways can you '
find the second answer? Which is the better way?)
2. If Jerry lies in bed 6 minutes every morning after
he is called, he loses in this way minutes in a
week ; in 2 weeks he loses minutes. (Do this second
part in three ways. Which is the best way?)
3. Jerry spends 12 minutes every morning before
school helping his mother. During the school week he
spends minutes in this way. How many hours is
this?
4. The walk from the house to the sidewalk is 11 feet
long. If Jerry clears this walk of snow 3 times in one
month he has cleared in all feet of walk. If during
the winter he clears this walk 9 times, he has during
the winter cleared in all feet. (Do this second part
in three ways. Which is the best way?)
5. Mother's napkins are i foot square. Then each one
contains square feet of cloth. A dozen napkins
contain square feet of cloth. Three dozen contain
square feet. (Do the last part in three ways,
selecting the best.)
Additional Work. Each pupil should write out and bring to class
a similar problem of his ovm.
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68 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XVII. READING NUMBERS
A. $10.01 $25.10 $17.60 $38.19 $47.85
B. $50.50 $60.05 $89.19 $75.25 $54.45
C. $90.09 $98.88 $77.77 $15.00 $30.00
XVIII. MULTIPLICATION
Note. Have pupils notice that the easy way to multiply by 10 is to
annex a zero to the multiplicand.
.4. 123945678
101010101010101010
B. 10 11 12 15 20 22 30 42 55
JL0_10J0_1010 10 10 10 10
XIX. MULTIPLICATION
Note. Have pupils notice that the easy way to multiply by a multiple
of 10 is to multiply first by the " significant " figure and then to annex as
many zeros asy.there are zeros in the multiplier. The zeros in the multi-
plier may lie to the right of or under the multiplicand.
A. 14
14
10
10
10 20
10
20
10
20
30 40
B 32
32
2
2
2 12
10
20
40
200
500 300
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GRADE IV. FIRST SERIES 69
XX. PROBLEMS: AT HOME
(When you read the following numbers be sure that you put and in
them at the right places.)
1. Mabel's father paid in house rent in a year |264. He
paid for his year's supply of coal $90.90. For an auto-
mobile he paid $795.
2. In Mabel's home each window has 12 panes of glass.
Then in 10 windows there are panes. In 20 windows
there are panes. (Do this second part in two ways.)
3. How many pounds of coal does Mabel's mother bum
in her kitchen stove in 10 days if each day she bums
12 pounds? How much will she bum in the month of
November? (Do the last part in two ways. Which way
is the easier?)
4. Mabel has invited 9 girl friends to a party. She
wants to have 4 cookies for everyone in the party. How
many cookies must she have?
5. She makes 6 bean bags with which to play games.
Into each bag she puts 200 beans. There will be
beans in the six bags.
6. If in Mabel's family 3 pounds of table butter are
used every week, in 10 weeks the family uses
pounds.
7. Mabel's mother preserves eggs in " water glass " in
5 jars. She puts 30 eggs in each jar. Then she preserves
eggs in all.
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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70 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XXI. READING NUMBERS
A. $101.01 $205.50 $100.25 $330.12
B. $200.10 $510.07 $601.75 $989.90
a $414.00 $800.86 4716.64 $555.55
XXII. DIVISION
Note. When both divisor and dividend end with a zero, teach pupils
to omit them both (in written work draw a line through them) before
dividing ; for example, 40 -^ 20 = 4 -s- 2.
A. lyi lOyiO 10)20 10)30 10)40
B. 10)110 10)240 20)60 2u)80 20)l20
a 30)30 30)60 30)90 30)120 50)50
XXIII. DIVISION
A. 18-«-9= 180h-90= 80 + 40= 210+30 =
B. 160 + 80= 270 + 90= 250 + 50= 180 + 60 =
a 240 + 30= 150 + 30= 220 + 110= 330 + 110 =
D. 160 + 40= 120 + 60= 240 + 20= 180 + 90 =
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GRADE IV. FIRST SERIES 71
XXIV. PROBLEMS: AT HOME
Note. When you read the following numbers be sure that you use and
only at the decimal points.
1. Elsa's father buys a piano for $350, a piano stool
for $4.50, and a music cabinet for $10.25. His bill for
the three purchases amounts to $364.75.
2. Elsa's father is a market gardener. He raised 400
bushels of potatoes and stored them in bins holding 20
bushels each. They filled bins.
3. One day Elsa's father takes to market 120 heads of
lettuce, which are packed in boxes, 20 heads in a box.
How many boxes of lettuce does he carry to market?
4. He has 220 pints of strawberries, which he puts
into 220 boxes. Each of the boxes must contain
pints of berries.
5. Elsa's mother has a piece of cloth that she wishes to
make into 10 towels. The cloth is 20 yards long. How
long is the cloth for each towel ? If she wanted to make
20 towels, how long would she cut each piece ?
6. The sidewalk in front of Elsa's house is 100 feet long.
How many boys must be hired to shovel the snow from
this walk if each boy is paid to shovel 50 feet ?
7. Elsa's father has 120 pounds of parsnips that he
wishes to put in boxes holding 20 pounds each. He will
need boxes.
Additional Work. Each pupil should write out and bring to class
a similar problem of his ovm.
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72 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XXV. PROBLEMS: MISCELLANEOUS
1. David lives at No. 708 Park Avenue, and Louise lives
at No. 819 Park Avenue. Read the numbers correctly.
2. It is house-cleaning time at David's home. Mother
plans to have the windows washed. There are 4 panes of
glass in each window. How many panes are there in 10
windows? (Do this in two ways, by counting by 4's and
by multiplying. Which is the easier way?)
3. David's father buys 17 tons of coal for winter. Of
this 10 tons is for the furnace, and the rest, tons,
is for the kitchen stove.
4. Louise is wiping the dishes for her mother. She
puts 3 plates on top of a pile of 4 plates, and later she
puts on the pile 3 more plates. How many are then
on the pile?
5. Uncle Henry gave Louise half a pound of chocolate
creams and her mother a pound of the same kind. Louise
counted her creams and found that there were 20 of them.
At the same rate how many creams would her mother
have ?
6. There are 24 hours in a day. Children should sleep
at least 9 hours a day. If they do, how many hours will
they have left for work and play ? How many hours will
they have for work and play in 20 days ?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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GRADE IV. FIRST SERIES 78
XXVI. PROBLEMS: MISCELLANEOUS
1. The children are playing ** Hide and Seek." Jack is
" it " and must stand still with his eyes shut while he
counts by 5's to 100. How quickly can you do this with-
out making a mistake ?
2. Hannah's mother usually fries 18 doughnuts on
Saturday, but company is coming and she thinks she
should have 28 doughnuts. She will need to fry
more than usual.
3. One day in vacation Jack is helping in the hay-
field. After the hay is all raked up they count 47
stacks. On the first load 12 stacks are pitched. That
leaves stacks in the field.
4. After two loads of hay have been taken from the
field 22 stacks are left. Then stacks have been
carried away on the two loads.
5. The farmer whom Jack is visiting has 20 cords
of wood that he has planned to sell in the city. He
expects to carry it in 10 loads of equal size. How
much will he load on the cart at one time?
6. This same farmer has 80 pecks of apples that he
puts into 20 boxes of equal size to carry to market.
Each box must hold pecks. This is the same as
bushels.
Additional Work. Each pupil shotdd write out and bring to class
a similar problem of his own.
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GRADE IV. SECOND SERIES
I. READING NUMBERS
Note. See Note, p. 60.
A. 1000 1100 1110 1101 1001
B. 2105 3060 2400 4075 5000
C. 3009 1090 4800 4999 2002
II. ADDITION
Note. Pupils should look at each combination carefully and give the
sums from left to right without naming the numbers to be added.
A. $1.08 $7.05 $9.08 $9.04 $8.20
.05 5.01 6.01 7.02 6.10
B. $9.40
5.10
$6.20
3.02
$6.05
5.05
$9.10
4.01
$9.70
3.10
a $8.00
7.00
$5.07
4.07
$9.09
8.09
$7.08
4.08
$8.06
3.04
III. ADDITION
A. $9.70 + 2.02 = $7.04 + 6.30 = $5.03 + 3.10 =
B. $7.06 + 3.06= $6.40 + 2.40= $5.08 + 2.04 =
C. $6.10 + 3.30= $8.07 + 2.05= $9.09 + 6.07 =
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GRADE IV. SECOND SERIES 75
IV. PROBLEMS: AT SCHOOL
1. Herbert goes to a large city school in which there are
40 schoolrooms. In this school 1610 pupils are enrolled.
There are 3040 pupils in one of the other schools of that
city. (Be careful about the use of and when you read
these numbers.)
2. All the things you use in school cost money. Who
pays for them ?
3. In Herbert's school it costs $5.60 to supply all the
pupils with pencils during the year, and to supply them with
erasers it costs $1.20. These two articles alone cost .
4. The desks cost $6.75 each and the seats $3.00 each.
What do a desk and seat together cost ?
5. If you lose or destroy a reader costing $0.35 and an
arithmetic costing $0.40, how much should you pay to the
teacher ?
6. It probably costs $8.00 to supply a set of readers
for your school and $9.00 to supply a set of arithmetics.
How much will these two sets cost?
7. If it costs $7.50 to supply your school with paper the
first half year and $6.40 the second half year, the paper
you have used during the year costs .
8. Have pupils find the cost of various articles used in
school and make original problems in addition.
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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76 PRACTICE EXERCISES IN MENTAL ARITHMETIC
V. READING NUMBERS
A. LI LII LIV LV LVII LIX LX
B, LXI LXIII LXX LXXI LXXIV LXXX LXXXI
a LXXXV XC XCI XCIV XCVI XCIX *C
VI. ADDITION
Note. Train pupils to look thoughtfully at each combination before
they attempt to state the sum. Let them then read the sums from left
to right.
A. $10.00
10.00
$0.10
, -10
$70.00
30.00
$0.70
.30
$75.00
25.00
B. $0.75
.25
$50.00
25.00
$0.50
.25
$5.25
5.25
$8.00
3.00
a $300.00
10.000
$30.00
10.00
$3.00
1.00
$0.30
.10
$0.03
.01
VII. ADDITION
A. $5.00 + 10.00= $32.15 + 32.15= $10.13 + 2.10 =
5. $60.00 + 40.00= $80.15 + 20.10= $17.30 + 3.03 =
C. $50.00 + 16.18= $50.00 + 50.00= $33.33 + 66.66 =
D. $11.22 + 44.33= $61.14 + 17.14= $15.15 + 15.15 =
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GEADE IV. SECOND SEEIES 77
VIII. PROBLEMS: AT SCHOOL
1. Look in your various schoolbooks and state where
Roman numbers are used.
2. Peter goes to a two-room school in the country.
Most of the children are carried to school in automobile
trucks. One man receives $12.00 a week for carrying the
children by one route and another receives $15.00 a week
for carrying them by another route. It costs a week
to transport these children to and from school.
3. A wall map of the United States is bought for
each of the rooms in Peter's school at a cost of $5.10
each. What do the two maps cost? (Do this in two
ways. Which is the better way?)
4. It costs $90.00 for coal to heat Peter's schoolhouse
in the winter and $10.00 for wood. The expense for heat
is then a year.
5. The janitor is paid $300.00 a year to care for the
school building, and brooms, brushes, and other janitor's
supplies cost $25.00. It costs to care for the building.
6. If the expense of repairing damages done to the
school furniture in Peter's room is $15.00 and to the
furniture in the other room is $10.00, the furniture-
repair bill for the year is .
7. The pupils in Peter's school raised $40.20 by giving
entertainments and $8.40 by a candy sale. How large
an amount did the children raise for the school?
Additional Work. Hack pupil should write out and bring to class
a similar problem of his own.
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78 PRACTICE EXERCISES IK MENTAL ARITHMETIC
IX. COUNTING
A. Count by 6's to 96.
B. Count by T's to 98.
X. SUBTRACTION
Note. Review pages 86 and 64 before taking this exercise.
A. $4.10
2.00
$4.90
1.90
$4.20
3.10
$4.80
2.40
$5.90
4.20
£. $7.00
3.00
$4.60
1.10
$6.90
2.30
$5.50
3.00
$5.00
2.00
C. $15.50
2.20
$0.75
0.40
$1.78
0.75
$8.50
0.25
$55.58
50.50
XL SUBTRACTION
A. $52.00-2.00= $52.00-22.00= $75.00-25.00 =
B. $1.18-0.18= $17.60-7.40= $30.15-15.15 =
C. $87.25-11.10= $84.14-24.04= $39.19-35.15 =
2>. $28.23-28.13= $60.40-50.20= $41.20-20.00 =
H. $99.99-33.33= $77.77-44.44= $70.85-60.40 =
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GRADE IV. SECOND SERIES 79
XII. PROBLEMS: AT SCHOOL
1. Paul is asked by his teacher to put 7 sheets of
paper on the front desk of each of the 6 rows in his
room. How many sheets does he need? (Find this out
by coimting by 7's and in one other way. Which way
is easier?)
2. In Hannah's room the desks are arranged in 7
rows, with 6 seats in a row. If Hannah puts 6 sheets
of paper on each front desk for a writing lesson and
6 sheets for an arithmetic lesson, she will need
sheets. (Find this by counting and in two other ways.
Which way do you prefer?)
3. In Hannah's school the paper used costs $22.50 a
year. Of this the pupils waste paper to the value of
$2.50. What is the value of the paper they use?
4. What is the difference in the cost of a teacher's desk
bought for $27.33 and a pupil's desk bought for $5.30 ?
5. When pupils lose pencils to the value of $0.25
out of a lot costing $6, what is the value of the pencils
they actually use?
6. If $84 is paid for coal for your school and only
$80 worth is used, what value of coal is left over iox
next year?
7. In Hannah's school an entertainment is given to
raise $35. Only $30 is raised, leaving to be raised
by gifts.
Additional Work, Each pupil should write out and bring to class
a similar problem of his own.
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80 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XIIL COUNTING
A. Count by 8's to 96.
B. Count by 9's to 99.
XIV. MULTIPLICATION
Note. Review pages 52, 66, and 68 before taking this exercise.
A. $9
2
$0.09
2
$6
3
$0.06
3
$6
4
$0.06
4
B. $12
2
$0.12
2
$11
7
$0.11
7
$10
6
$0.10
6
a $8
3
$0.12
6
$0.07
7
$7
4
$11
6
$0.08
6
XV. MULTIPLICATION
A. $12.00x9= $8.00x8= $12.00x5= $9.00x8 =
B. $0.09x5= $0.08x6= $0.08x7= $0.09x4 =
a $1.11x2= $3.30x3= $15.00x2= $15.15x2 =
2). $50.00x2= $25.25x3= $30.20x3= $10.11x4 =
K $14.14x2= $9.09x5= $8.08x6= $9.10x9 =
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GRADE IV. SECOND SERIES 81
XVI. PROBLEMS: AT SCHOOL
1. If a pad of paper costs $0.06 and there are 9
pupils in a class, how much does it cost to supply the
class with pads?
2. There are 9 sets of books, in each of which there
are 8 books that need rebinding at the end of the
year. In all the sets there are books that need
rebinding. (Do this by counting and in one other way.
Which is the better way?)
3. What is the cost of putting new covers on 8 books
at $0.11 a book?
4. The janitor puts a new box of crayons in each
schoolroom at the beginning of the year. How much
does it cost to supply a two-room building at $0.20 a box ?
(Do this last part in two ways. Which is the easier ?)
5. It costs $0.25 to replace a broken pane of glass.
How much should boys pay who break 3 panes?
6. Paul has carelessly scratched his desk. It costs
$1.10 to repair the damage. If there are 5 careless
children in school who damage their desks as Paul did,
how much of the taxpayers' money have they wasted?
7. If it costs $7 to' buy a set of readers for your
class, how much will it cost to supply 6 classes at the
same price?
8. John's pencils cost $0.06 each. If he loses 4 of
them in a year, how much money has he wasted?
Additional Work. Each pupil shovld write out and bring to class
a similar problem of his own.
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82 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XVII. COUNTING
A. Count by ll's to 99.
B. Count by 12's to 96.
XVIII. MULTIPLICATION
A. $9
12
$8
8
$0.05
12
$0.08
9
$0.05
9
$0.06
8
B. $4.00
9
$7.00
7
$8.00
8
$6.00
6
$5.05
8
$6.06
9
a $7
10
$7
20
$7
30
$8
40
$9
ioo
$10
10
D. $7.07
9
$4.04
8
$6.06
11
$4
70
$11
11
$22
40
XIX. MULTIPLICATION
A. $12x12= $11x30= $0.12x6= $0.03x7 =
B. $0.02x8= $2.02x6= $4.04x8= $9x3 =
C. $9.09x11= $60x10= $6x50= $8.08x11 =
2>. $9.09x9= $12x50= $11x80= $10x20 =
K $12x9= $12x5= $0.09x8= $0.09x5 =
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GRADE IV. SECOND SERIES 88
XX. PROBLEMS: AT SCHOOL
1. How many ll's do you count if you start with 11
and count to 99 ? Which is easier, to count by ll's to
99 or to multiply 11 by 9? Try it before you answer.
2. How many pencils are there in a bundle contain-
ing a dozen? The teacher sends Charlotte to the supply
room to get 8 dozen pencils. Count them for her as
she takes each package and state the number of pencils
she will have.
3. The school board has decided to put new seats
and desks in Charlotte's room. There is room for 40
pupils, and the seats and desks together cost $8 each.
The new seats and desks cost .
4. New window shades also are put up in Charlotte's
room. There are 5 windows, and each shade costs $0.20.
It costs to supply the shades.
5. The janitress is paid $1 a day to take care of the
little country school that Charlotte attends. A school
week for the janitress is 6 days. She receives a
week. For a fortnight she receives . Her pay for
a month is . (Do this last part in three ways and
select the easiest way.)
6. Charlotte's teacher is paid $90 a month. How
much is that for a school year of 10 months?
7. If the teacher pays $10 a week for board during
the school year of 40 weeks, she will pay .
Additional Work. Each pupil should vrrite out and bring to class
a similar problem of his ovm.
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84 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XXL READING FRACTIONS
^. i f I I I i f t i
XXIL DIVISION
Note. In this exercise the divisors are abstract. The division separates
the dividend into parts ; that is, the quotient is a certain part (represented
by the divisor) of the dividend. Review pages 40, 54, and 70.
A, 2)|2 5)$5 2)$0.02 3)$0.03 3)$3
B, 10)$10 lOjIoIO 2)$al0 20)$20 20)|0^
a 9)$0.18 7)$0.49 8)$8.08 5)$25.10 6)$12.30
XXIIL DIVISION
Note. In this exercise the divisors are the same kind as the dividends.
The quotients are therefore abstract, representing the number of times that
the divisor is contained in the dividend.
A. $2)f2 $5)|5 $6)|60 $12)$72 $0.02)$0:02
B. $11)199 $0.11)1099 $9)$36 $20)$40 $30)$60
a $0.10)$0;20 $10)$20 $5)|50 $0.05)$0^
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GRADE IV. SECOND SERIES 85
XXIV. PROBLEMS: AT SCHOOL
1. Half a dozen pointers have been bought for use
at the blackboard in your school at a cost of $0.60.
If you break one, how much ought you to pay for it?
2. It may cost $0.75 to put curtains at the three
windows of your schoolroom. If one is broken, how
much will it cost to replace it?
3. The pencils like those that Paul uses in school cost
$0.06 at the store. How many can he buy with $0.06?
4. Paul has $0.18 with which he wants to buy as
many pencils hke those he uses in school as he can.
He can buy pencils with his $0.18. (Do this by
counting and in one other way. Which way is easier?)
5. $0.99 is paid for blackboard erasers. If each one
costs $0.11, how many are bought ? (In what two ways
can you do this? Which is easier?)
6. If in a four-room building the pupils could save
for the taxpayers $16 by avoiding waste, what would
the share of saving be for each room? How could the
pupils avoid waste? What would the money saved buy
that would be useful in your school?
7. At the close of the school year 6 desks in Paul's
room are so badly scratched that they are refinished at
a cost of $6.60. How much has each of the six careless
children cost the taxpayers?
Additional Work. Each pupil should write out and bring to class
a similar problem of his ovm.
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86 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XXV. PROBLEMS: MISCELLANEOUS
1. In Jane's and Harry's school it was decided to
hold a Christmas sale. At Jane's table $9.30 was re-
ceived from the sale of candy, and at Harry's table
$7.20 was received from the sale of toys. At both tables
was received.
2. Anna was at the head of the table where boys' neck-
ties were sold. She sold 9 of them at $0.11 each, receiving
in all for the neckties.
3. Some of the boys fixed up a side show. $0.05 was
charged for entrance tickets. Stephen, who was door-
keeper, found that he had taken in 15 nickels. By count-
ing by 5's he found that he had received cents in
nickels. Could he have found out more quickly in some
other way than by counting ?
4. Susan sold 20 Christmas cards for which she received
$0.40. If they were all sold at the same price, what was
charged for each one ?
5. The Christmas cards that were sold for $0.40 were
purchased at a friendly stationer's for $0.20. So the profit
that went into the school funds was .
6. When the Christmas sale was over, all the money
received was counted. It was found that $25.00 had been
taken in at tables and side shows and $10.25 had been
taken by the sale of admission tickets. In all that
made .
Additional Work. Each pvpil shcndd tmte out and bring to class
a similar problem of his oum.
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GRADE IV. SECOND SERIES 87
XXVI. PROBLEMS : MISCELLANEOUS
1. Ink is often bought for schools by the gallon. If
$0.80 is paid for a gallon, how much does it cost to fill
a quart bottle for Roland's room ?
2. Paper is bought by the school committee in
packages containing 500 sheets. In 5 packages there
are sheets.
3. Viola is asked by her teacher to give 2 sheets of
paper to each of the 42 pupils in her room. Find out
by coimting by 2's how many sheets she needs. Find
out in an easier way than by counting.
4. If $0.23 is paid for each package of paper in a
school, how much has it cost the taxpayers to supply
your room with 3 packages?
5. Suppose that in one month the pupils in your school
could save $1.00 by being careful in the use of supplies.
At the end of the school year of 10 months they will
have saved .
6. In Harold's school it is decided to buy some play-
ground apparatus. The cost is looked up, and it is found
that a football costs $3.10 and that a basket ball costs the
same. If one of each is bought the school must raise .
7. For baseball 2 bats are needed costing $0.25 each
and a ball costing $0.50. How much more must be raised
if the school decides to play baseball?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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GRADE IV. THIRD SERIES
I. READING MIXED NUMBERS
Note. When reading mixed numbers the word and should be used only
between the whole number and the fraction. 101^ is read ''one huudred
one and one half." See Note, p. 66.
A. li
^
H
H
H
6|
7|
B. 9f
10|
15|
18|
20i
50|
98i
II. FRACTIONAL PARTS
^. ^ of 1 = I of 2 = i of 4 = i of 10 =
5. ^ of 1 = i of 3 = i of 6 = ^ of 12 =
C. J of 1 = -1- of 4 = i of 8 = J of 16 =
D. ^ oi 9= I of 14 = J of 12 = ^ of 15 =
III. FRACTIONAL PARTS
^. J of 20 = i of 24 = J of 28 = J of 36 =
A i of 24 = i of 30 = ^ of 36 = ^ of 60 =
C. J of 40 = ^ of 50 = i of 80 = ^ of 100 =
D. ^ of 60 = ^ of 75 = J of 88 = J of 100 =
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GRADE IV. THIRD SERIES 89
IV. PROBLEMS: AT THE NEWSDEALER'S STORE
1. Harold is a newsboy who buys his papers of
Mr. Carlton at No. 7014 Main Street. Harold pays 1^^
for some papers and IJ^ for others. He wears a badge
that has the number 82 on it.. Read the numbers
correctly.
2. One day Harold bought 30 papers, but only sold
^ of them. Then he sold papers.
3. Mr. Carlton put 3 dozen bottles of ink on his
shelf and sold J of them in a week. How many ink
bottles did he sell in a week?
4. If there are 4 jars of candy on the shelf and J
is broken, there are jars remaining on the sheK.
5. Mr. Carlton buys 100 papers every night, but
sells only ^ of them in the store, selling the rest through
newsboys. Then he sells papers in the store, and
the newsboys sell papers.
6. If Mr. Carlton tells Harold to put the 4 dozen
magazines on 4 shelves, an equal number on each shelf,
he should put magazines on each shelf. (The
answer may be given in two ways.)
7. Every week Harold sells 22 Saturday Evening
Posts. . Of these he delivers ^ at the homes of regular
subscribers and the rest he sells on the street. Then
he has regular customers.
Additional Work. Each pupil should write out and bring to class
a similar problem of his otvn.
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90 PRACTICE EXERCISES IN MENTAL ARITHMETIC
V. COUNTING BY FRACTIONS
Note. This and similar exercises will familiarize pupils with the names,
sequence, and relative value of fractions. The pupils will say, " ^, | or 1 ;
f, J or 2; "etc.
A. Count by halves to 10.
B. Count by thirds to 10.
VI. MEASURES OF LENGTH
A. 1 ft. = ? in. 2 ft. = ? in. 3 ft. = ? in.
5. J ft. = ? in. ^ ft. = ? in. ^ ft. = ? in.
a 1yd. =? ft. 2 yd. = ?ft. 5 yd. =?ft.
D. 1 yd. = ? in. ^ yd. = ? in. J yd. = ? in.
K 1^ ft. = ? in. 11 ft. = ? in. IJ ft. = ? in.
VIL MEASURES OF LENGTH
A. 12 in. = ? ft. 18 in. = ? ft. 24 in. = ? ft.
B. 3 ft. = ? yd. 6 ft. = ? yd. 9 ft. = ? yd.
C. 36in. = ?yd. 18in. = ?yd. 9in. =?yd.
D. 24 in. = ? ft. 36 in. = ? ft. 18 in. = ? ft.
K ? in. = ^ yd. ? ft. = ^ yd. ? in. = i yd.
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GRADE IV. THIRD SERIES 91
VIII. PROBLEMS: AT THE DRY-GOODS STORE
1. The clerk behind the ribbon counter is cutting a
long piece of ribbon in half-yard lengths. After she
has cut 8 such lengths, she has used yards of
ribbon. (Find the number of yards by counting by
half-yards.)
2. If the clerk cut the ribbon into 12-inch lengths,
how many yards would she use in cutting 3 lengths?
(Find this answer in three ways and choose the easiest
way.)
3. The clerk at another counter sells IJ yards of
silk. How many inches more than a yard is that?
4. A tape measure is generally 60 inches long. One half
of it is how many inches long?
5. A piece of cloth is 24 inches in width. How
many feet wide is it?
6. If a piece of cloth is J yard wide, how many
inches wide is it?
7. If a boy wears a 13-inch collar, what will it
measure in feet and inches?
8. Anna buys enough ribbon to make a bow 2 feet
long. How many inches does the clerk measure off?
How many inches less than a yard does Anna buy?
What part of a yard is left?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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92 PRACTICE EXERCISES IN MENTAL ARITHMETIC
IX. COUNTING BY FRACTIONS
A. Count by fourths to 10.
B. Count by fifths to 10.
X. MEASURES OF AREA
A. 1 sq. ft. = ? sq. in. 2 sq. ft. = ? sq. in.
B. 1 sq. ft. = ? sq. in. J sq. ft. = ? sq. in.
a 1 sq. yd. = ? sq. ft. 2 sq. yd. = ? sq. ft.
D, 3 sq. yd. = ? sq. ft. 5 sq. yd. = ? sq. ft.
K 10 sq. yd. = ? sq. ft. 20 sq. yd. = ? sq. ft.
XL MEASURES OF AREA
A, 144 sq. in. = ? sq. ft. 288 sq. in. = ? sq. ft.
B, 72 sq. in. = ? sq. ft. 36 sq. in. = ? sq. ft.
a 9 sq. ft. = ? sq. yd. 18 sq. ft. = ? sq. yd.
D. 36 sq. ft. = ? sq. yd. 90 sq. ft. = ? sq. yd.
U. How many inches around (perimeter) 1 sq. in.?
F, How many feet around 1 sq. ft.?
G. How many yards around 1 sq. yd.?
H. How many feet around 1 sq. yd.?
I. How many inches aroimd 1 sq. ft.?
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GRADE IV. THIRD SERIES 98
XII. PROBLEMS : AT A HARDWARE STORE
1. The hardware dealer sells and uses foot-rule measures.
Take your ruler and count by fourth (or quarter) inches to
the 3-inch division line. How many quarter inches are
there? What is an easier way of finding the niunber of
quarter inches in 3 inches?
2. Stephen goes to the hardware store and asks for
a square yard of mosquito netting. How many yards long
will it be ? How many yards wide ?
3. If the dealer uses a foot rule to measure the netting
for Stephen, how many feet will he measure oflE for the
length and the width?
4. How many square feet will Stephen's netting contain ?
5. What is the perimeter of Stephen's netting in yards ?
in feet ? (Find the perimeter in two ways. Which is the
easier way ?)
6. One day Stephen breaks a pane of window glass. He
measures the old glass and finds that it measures 12 inches
in length and 12 inches in width. He must pay for the
area of glass he needs. How many square inches must he
buy ? This is how many square feet ?
7. Stephen must also buy putty to fasten the glass in
place. How many inches in length must he apply the
putty? How many feet?
Additional Work, Each pupil shovJd write out and bring to class
a similar problem of Ms own.
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94 PRACTICE EXEBCISES IN MENTAL ARITHMETIC
XIII. MEASURES OF SOLIDS
A. 1 cu. ft. = ? cu. in. 1 cu. yd. = ? cu. ft.
B. How long is a cu. ft.? a cu. yd.?
C. How wide is a cu. ft.? a cu. yd.?
D. How high is a cu. ft.? a cu. yd.?
XIV. MEASURES OF LIQUID
A. 1 pt. = ? gi. 2 pt. = ? gi. 3 pt. = ? gi.
B. 4 pt. = ? gi. 1 qt. = ? pt. 2 qt. = ? pt.
C. 1 gal. = ? qt. 2 gal. = ? qt. 10 gal. = ? qt.
D. 2 gi. = ? pt. 1 gi. = ? pt. 3 gi. = ? pt.
E. 2 pt. = ? qt. 1 pt. = ? qt. 3 pt. = ? qt.
F. 4 pt. = ? qt. 4 qt. = ? gal. 1 qt. = ? gal.
XV. MEASURES OF DRY SUBSTANCES
A. 2 pt. = ? qt. 4 pt. = ? qt. 3 pt. = ? qt.
B. 8 qt. = ? pk. 4 qt. = ? pk. 16 qt. = ? pk.
C. 4 pk. = ? bu. 8 pk. = ? bu. 2 pk. = ? bu.
D. ^ bu. = ? qt. ^ bu. = ? pk. i pk. = ? qt.
K l|bu. = ?pk. lipk. = ?qt. 3pk. = ?qt.
F. 2bu. = ?pk. 2bu. = ?qt. 10bu. = ?pk.
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GRADE IV. THIRD SERIES 96
XVL PROBLEMS: AT THE PROVISION STORE
1. In Mr. Harper's provision store there is a big
block of wood on which he chops his meat. It meas-
ures 3 feet across one way, 3 feet across the other way,
and is 3 feet thick. How large would you say this
block is? (The answer may be given in two ways.)
2. On a shelf that is 12 inches wide Mr. Harper
wants to put a box that he finds measures a cubic foot.
How far apart must the shelves be and how much
space on the shelf will the box take?
3. Mr. Harper buys a bushel of green peas from a
farmer, but he sells them by the quart. How many
quarts can he sell from the bushel?
4. A barrel of apples is 2^ bushels. How many pecks
should Mr. Harper be able to sell out of the barrel?
5. Vinegar is bought by Mr. Harper in a keg holding
10 gallons. If his customers buy vinegar by the quart,
he can draw off quarts from his keg.
6. Mr. Harper has 20 customers that buy a quart of
milk a day in glass jars. How many gallons of milk
does that amount to?
7. Out of a box containing a bushel of potatoes
Mr. Harper sells a peck. Then pecks remain in
the box.
AdHtianal Work. Each pupil should write out and bring to class
a similar problem of his own.
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96 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XVIL MEASURES OF WEIGHT
A. llb. = ?oz. Jlb. = ?oz. ^lb. = ?oz.
5. 1 T. = ? lb. ^ T. = ? lb. 2 T. = ? lb.
a 16oz. = ?lb.
D. 2000 lb. = ? T.
8 oz. = ? lb.
1000 lb. = ? T.
4 oz. = ? lb.
30001b. = ?T.
XVIII. MEASURES OF TIME
A. 1 min. = ? sec. ^ min. = ? sec. J min. = ? sec.
^ hr. = ? min. ^ hr. = ? min.
1 da. = ? hr. 2 da. = ? hr.
1 wk. = ? da. 2 wk. = ? da.
1 yr. = ? wk. 1 yr. = ? mo.
B. 1 hr, = ? min.
C. 1^ hr. = ? min.
D. ^ da. = ? hr.
K 1 yr. = ? da.
XIX. MEASURES OF TIME
A. 60 sec. = ? min. 30 sec. = ? min. 15 sec. = ? min.
90min. =?hr.
24 hr. = ? da.
7 da. = ? wk.
6 mo. = ? yr.
B. 60min. = ?hr,
C. 15 min. = ? hr
D. 48hr. = ?da.
H. 365da. = ?yr.
30 min. = ? hr.
12 hr. = ? da.
4 wk. = ? mo.
52 wk. = ? yr.
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GRADE IV. THIRD SERIES 97
XX. PROBLEMS: AT THE BAKESHOP
1. Anna buys a large loaf of bread (1-pound loaf) at
the baker's. How many ounces of bread does she buy?
2. The baker buys a ton of flour. If he bakes it
into bread, putting a pound of flour into each loaf, he
will bake loaves.
3. If the baker makes another ton of flour into loaves
containing half as much flour, he will make small
loaves.
4. Each kind of food the baker makes requires a
particular length of time for baking. If it takes f hour
to bake bread, how many minutes does it require?
5. But to make good bread it must be *' raised."
This requires about ^ day, or hours.
6. One man has worked for Mr. Harris, the baker,
a whole year without one day off. How many days
has he worked?
7. If a man takes 1 day off each week, he works
days in the year.
8. A working day is one third of a whole day. How
many hoiKS a day does a man work?
9. If the clerk in the bakeshop has | hour for lunch
at noon, he is away from the store minutes.
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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PRACTICE EXERCISES IN MENTAL ARITHMETIC
XXI. COUNTING
2 doz. = ? units
J doz. = ? units
1 gro. = ? units
18 units = ? doz.
24 units = ? doz.
144 units = ? gro,
A. 1 doz. = ? units
B, ^ doz. = ? units
C 1 gro. = ? doz.
D. 12 units = ? doz
E. 4 units = ? doz.
F. 12 doz. = ? gro.
3 doz. = ? units
^ doz. = ? units
\ gro. = ? doz.
6 units = ? doz.
3 units = ? doz.
6 doz. = ? gro.
XXII. MEASURES OF PAPER
A, 1 quire = ? sheets ^ quire = ? sheets \ quire = ? sheets
B. 1 ream = ? sheets 2 reams = ? sheets ^ ream = ? sheets
C. 24 sheets = ? quires 6 sheets = ? quires
36 sheets = ? quires
D, 500 sheets = ? reams 250 sheets = ? reams
1000 sheets = ? reams
XXIII. MEASURES OF UNITED STATES MONEY
A, 1 ct. = ? mills 2 ct. = ? mills ^ ct. = ? mills
5d.= ?^
$1.00 = ? ^
$1.00 = ? d.
B. 1 d. = ? ^
C. 10 d. = ? ct.
D. $i=?^
E. 10 mills = ? ct.
F. 5^=?d.
5 mills = ? ct.
100^ = ? $
8d. = ?^
$i = ? ct.
$i = ?d.
10^ = ?d.
50^ = ? $ ? d.
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GRADE IV. THIRD SERIES 99
XXIV. PROBLEMS : AT THE STATIONERY STORE
1. Mr. Morris keeps a stationery store. He buys pencils
by the gross. If he buys two gross of Faber's pencils, how
many pencils does he buy ? How many dozen pencils ?
2. Arthur buys half a dozen pencils. Mr. Morris counts
out pencils from a package containing 1 dozen.
3. If Mr. Morris buys 1 gross of small ink bottles and sells
6 dozen of them, he has dozen left, or bottles.
4. Mr. Morris opens a package of paper containing a
ream and sells half of it. He should have sheets
remaining in the package.
5. A customer buys 2 quires of paper. How many
envelopes will he need if he plans to put only one
sheet in each envelope? (Envelopes generally are sold
in packages. How many are there in a package?)
6. Arthur gives Mr. Morris a dime when he buys a
5^ pencil. He should receive ^ in change.
7. If Mr. Morris sells 10 paper napkins for 1^, each
costs mills. You can buy napkins for a dime.
8. Arthur receives 5 dimes as change one day when
he buys some stationery for his mother. How many
cents might Mr. Morris have given him?
9. If Arthur had received his change, amounting to
5 dimes, in one piece of money, he would have received
dollar.
Additional Work, Each pupil should write out and bring to class
a similar problem of his owru
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100 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XXV. PROBLEMS: MISCELLANEOUS
1. Alan went to the grocery store and bought -|- dozen
eggs and ^ pound of butter. How many eggs did the
grocer count out for him and how many ounces of butter
did he weigh out on the scales ?
2. The fruit man sells 2 apples for 1^. That is at the
rate of one apple for ^, or mills.
3. If you buy 2 reams of paper how many sheets will
you buy ?
4. The owner of a candy store buys of the wholesale dealer
a box of candy containing 100 pieces. The pieces are packed
in 5 layers. There must then be pieces in each layer.
5. Mother asks Gertrude to take the tape measure and
measure off 2 yards of a piece of cotton cloth that she
has bought. How many inches does she measure off ?
6. Chester is sent to the hardware store to buy a piece of
2inc to put under his mother's stove. It is to be a square
yard in size. What will it measure on the four sides ?
7. Suppose you are a clerk in a bakeshop. Count out
3 dozen doughnuts by 2's ; by 3's ; by 4's.
8. Chester buys at the hardware store 5 screws for 1^.
That is at the rate of 1 screw for mills.
9. Chester pays 20^ for some ribbon for his sister and
gives the clerk $1.00. His change is all in dimes. How
many does he receive ?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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GRADE IV. THIRD SERIES 101
XXVI. PROBLEMS: MISCELLANEOUS
1. Viola goes to the grocery store and buys cream in
a small bottle holding one-half pint. How many gills
of cream does she buy?
2. The grocer has in his refrigerator 20 pint bottles
of milk. How many quarts does that make?
3. If he has 2 gallons of milk in a can, he can sell
from it quarts.
4. The provision dealer has a box containing a bushel
of potatoes. He sells Arthur a peck. He has pecks
left in the box. How many quarts of potatoes are left?
(Do this in two ways and decide which is the easier way.)
5. The provision dealer has an ice box that measures
inside 3 feet in length, 3 feet in width, and 3 feet in
depth. How many cubic yards of ice will it contain?
How many cubic feet of ice?
6. Mr. Harris, the market man, has 500 pounds of
ice put in his refrigerator every week. In how many
weeks does he use 1 ton of ice?
7. Viola happened to be in a jeweler's shop when the
jeweler was setting a watch that was a Kttle slow. He
sets it forward one-half minute, or seconds.
8. The clerk in the bakeshop has a two weeks' vaca-
tion in summer. That is month, or days.
9. If John, the provision clerk, works 10 hours a
day, that leaves him hours for himself.
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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GRADE IV. FOURTH SERIES
I. TWO PEOCESSES
A, 2 + 4-1= 18-10 + 9= 16-9 + 7= 6 + 9-7 =
B, 18-8 + 7= 5 + 8-6= 15-7 + 6= 13-7 + 7 =
II. ADDITION
Note. Have pupils note the numbers that in sequence make 10 before
they begin to add. This should become a habit in all addition. Encourage
adding other combinations also ; that is, 3 + 1, 2 + 1, 2 + 2, 3 + 2, etc.
A. 5
7
9
3
2
3
3
2
5
3
3
7
7
4
■ 4 8
1
1
3
1
5
3
4
5
6
1
5
5
1
2 5
B. 6
6
1
2
7
7
1
5 5
3
3
7
5
8
4
3
2 4
1
1
3
5
2
6
7
8 1
8
4
3
7
3
3
2 7
III.
ADDITION
A. 2
7
9
2
5
7
6
5 4
8
3
5
3
7
1
2
1 4
3
6
3
8
3
1
1
2 2
9
4
2
2
5
1
1
2 2
B. 3
6
1
2
2
5
6
7 9
3
4
9
■ 2
7
6
8 6
7
6
7
2
1
8
6
5 7
3
8
2
4
4
2
4
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GRADE IV. FOURTH SERIES 108
IV. PROBLEMS OF THE CONDUCTOR
1. The conductor on a street car or a railroad train is
obliged to do a great many examples. In one freight train
there are 3 box cars, 4 platform cars, 6 tank cars, and 1
caboose. The conductor reports cars in his train.
2. Hilda rode from New York to Chicago in a train
consisting of (besides the engine) 1 baggage car, 1 smok^
ing car, 4 parlor cars, and 6 coaches. The engine drew
cars in this train.
3. Nelson was riding on a train that made four stops.
How many people got off if 8 people stopped at the
first station, 2 at the second, none at the third, and 5
at the fourth?
4. At one stop a number of people get on a street car.
After the car has started, the conductor finds that he
has received 4 tickets, 3 cash fares, 3 transfers, besides
7 passes from policemen and others who ride without
paying fares. Then people got on at that stop.
5. A motorman makes 4 trips a day, each trip taking
3 hours. How long does he work each day? (Do this
in two ways, selecting the easier way.)
6. A conductor is obliged to stop his train four times
during one trip. At the first stop he loses 3 minutes,
at the second 7 minutes, at the third 7 minutes, and
at the fourth 3 minutes. How late is his train at the
end of the trip?
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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104 PRACTICE EXERCISES IN MENTAL ARITHMETIC
V. TWO PROCESSES
A. 3 + 9-5= 17-8 + 9= 15-7 + 3= 16-8 + 8 =
B. 4 + 8-7= 15-8 + 3= 21-7-7= 4 + 6 + 10 =
a 12-7 + 6= 11-8 + 5= 14-2 + 7= 7 + 7 + 2 =
VI.
ADDITION
A. 2
5
7
8
4
6
7
2
3
7
3
1
2
5
3
2
4
1
2
6
4
7
5
3
4
6
9
4
5
6
3
6
7
3
4
1
5
3
4
4
B. 4
3
2
5
6
8
7
3
2
4
6
3
7
1
2
3
2
2
4
3
3
1
1
1
3
3
8
2
8
8
4
1
1
3
7
5
5
2
2
5
4
3
9
VII.
ADDITION
A. 4
5
9
6
5
7
2
5
6
1
4
3
2
6
2
4
8
5
4
7
8
7
2
6
5
1
5
1
5
3
4
5
1
6
9
5
7
7
B. 8
7
2
1
4
3
9
6
5
9
9
3
1
6
7
6
3
2
4
1
1
9
8
4
7
7
8
6
4
2
3
5
6
7
7
8
6
8
7
5
4
8
3
1
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GRADE IV. FOURTH SERIES 106
VIII. PROBLEMS OF THE POST OFFICE
1. If Mr. Casey, the letter carrier, has a bundle con-
taining 14 letters and delivers 2 letters at one house
and 2 at another, he has letters left to deliver.
(Do this in two ways and select the easier way.)
2. The postmaster has in his stamp drawer 21 two-cent
stamps. He sells 11 of them, but later puts 5 more in
the drawer. There are then in the drawer two-
cent stamps.
3. Five people buy two-cent stamps at the post
office. How many have they bought when the first
has purchased 5 stamps, the second 5, the third 2, the
fourth 3, and the fifth 5?
4. At different times during the day mail bags come
to the office with letters and papers from different parts
of this country. If 4, 4, 2, 7, and 3 bags are brought at
different times during the day, the office receives in all
bags.
5. On one trip the letter carrier delivered 3 parcel-
post packages at one house, 1 package at another, and 3
packages to each of three other places. In all he deliv-
ered on that trip parcel-post packages. (Do this
in two ways and select the easier way.)
6. In a large city there are five branch post offices.
There are 5, 5, 6, 3, and 7 carriers connected with the
several offices. This city has letter carriers.
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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106 PRACTICE EXERCISES IN MENTAL ARITHMETIC
IX. TWO PROCESSES
Note. In this and all similar exercises have pupils perform the multi-
plication and division processes before the addition and subtraction ; other-
wise perform the operations in the order of their occurrence.
A. 6-^2 + l= 8-^2 + 2= 8 + 2-5-2= 4 + 9-i-3 =
B. 12h-4-2= 70^10-5= 18-8^2= 24-7^7 =
a 254-6^3= 27"9-f-3= 15^5-h3= 27-9-2 =
X. MAKING CHANGE
Note. Pupils should make change as storekeepers do, by adding to the
amount of the purchase enough to equal the amount given by the pur-
chaser. That is, if $0.25 is given for a $0.03 purchase, the storekeeper
will say, "$0.03 and $0.02 are $0.05; $0.05 and $0.10 are $0.15, and
$0.10 are $0.25."
Pupils should be given freedom to make any practical combinations.
In the following the lower number represents amount of sale :
A. $0.10 $0.25 $0.20 $0.35 $0.30 $0.50 $0.50
0.02 0.17 0.16 0.26 0.21 0.30 $0.12.
B. $0.25 $0.25 $0.25 $0.45 $0.45 $0.35 $0.25
0.08 0.18 0.06 0.37 0.39 0.29 0.12
XL MAKING CHANGE
1. $0.50
0.25
$0.60
0.51
$0.75
0.50
$0.85
0.79
$0.90 $0.95 $1.00
0.81 0.86 0.50
(, $0.50
0.17
$0.50
0.28
$0.75
0.60
$0.70
0.61
$0.50 $0.65 $1.00
0.35 0.58 0.65
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GEADE IV. FOURTH SERIES 107
XII. PROBLEMS OF THE FRUIT SELLER
1. Mr. Rossi keeps a fruit stand. In a box there are
25 oranges. He puts 5 more with them and then divides
them into three equal lots of oranges each.
2. If the fruit dealer has 24 boxes of grapes, sells 4
boxes, and divides the rest into two lots, one of which
he puts in a dark room, how many boxes does he leave
on sale?
3. Clara buys a banana for $0.02 and gives $0.10 in
payment. Find her change.
4. What change does Mr. Rossi return to Tony, who
gives him $0.25 for a $0.03 orange?
5. A customer buys a dozen lemons costing $0.36. Count
out his change for $1.00.
6. If $0.50 is given in payment for grapes costing $0.15,
what is the change ?
7. Rosa buys of Mr. Rossi a pound of dates for $0.12.
What change does she receive if she gives him $0.20 ?
8. What change does Mr. Rossi give a customer who
gives him $0.75 for fruit costing $0.52?
9. Mr. Rossi has 90 grapefruit that he arranges in his
show window in three piles of equal size. He sells 6 grape-
fruit from one pile. How many are left in that pile ?
Additional Work. Each pupil sfwidd write out and bring to class
a similar problem of his own.
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108 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XIII. TWO PROCESSES
A. 3 + 2x2= 4-1x3= 4x10-5= 8h-4x6 =
B. 7-8-s-2= 4-5-4x6= 12-1-4 + 2= 5x5 + 2 =
C. 6^3-8-2= 3x4x2= 39-i-13-2= 16-4-5-4 =
D. 8x5-5-4= 42-5-6x5= 10 + 6x3= 4-20-5-5 =
XIV. MULTIPLICATION
A. $0.03
6
$0.05
11
$0.06
6
$0.04
11
$0.05
8
$0.04
6
B. $0.07
11
$0.05
6
$0.06
11
$0.03
8
$0.08
11
$0.05
9
a $0.03
9
$0.05
7
$0.09
11
$0.03
12
$0.04
8
$0.10
10
D. $0.04
12
$0.09
9
$0.07
7
$0.05
12
$0.06
7
$0.04
9
XV. MULTIPLICATION
A. $0.06x8= $0.06x12= $0.08x8= $0.06x9 =
B. $0.09x12= $0.08x9= $0.12x12= $0.07x8 =
a $0.07x12= $0.07x9= $0.08x12= $0.10x12 =
D. $0.10x11= $0.11x12= $0.11x11= $0.09x8 =
E. $0.12x11= $0.11x10= $0.12x10= $0.09x7 =
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GRADE IV. FOURTH SERIES 109
XVI. PROBLEMS OF THE DAIRY
1. If Mr. Jones has 4 cows, each of which gives 12
quarts of milk a day, how many gallons of milk do
they give? (This may be done in two ways. Which is
the easier?)
2. If one of Mr. Jones's cows gives 13 quarts of milk
a day, and he keeps 3 quarts for family use, how many
customers can he supply with 2 quarts each?
3. Mr. Jones feeds daily 5 quarts of skim milk to each
of 3 pigs. In 10 days the pigs will drink quarts.
4. If a milkman sells cream for $0.20 a half pint,
how much will Mrs. Mathews pay him if she buys
half a pint each week for a month?
5. If milk is $0.09 a pint, how much is it a quart?
a gallon? (The last part may be done in two ways.)
6. Mr. Jones sells milk to a milkman for $0.06 a
quart in large cans containing 9 quarts. How much
does he receive per large can?
. 7. If a farmer pays to an expressman $0.04 a can to
take his milk to the railroad station, where it is shipped
to the city, it will cost him to send 11 cans.
8. Mr. Jones puts up some of his milk in quart bottles.
If each bottle costs $0.05, he will pay for a dozen
bottles. If one of the dozen is broken and he buys an
extra bottle to take its place, he will pay for bottles.
Additional Work. Each pupil should write out and bring to class
a similar problem of his own.
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110 PRACTICE EXEECISES IN MENTAL AEITHMETIC
XVII. FRACTIONAL PARTS WITH REMAINDERS
Note. Pupils may state the remainders as whole numbers or as frac-
tions, as the teacher may direct; that is, J of 5 = 2 and 1 over, or 2\.
^. ^ of 3 = i of 7 = i of 9 = i of 11 =
^. ^ of 4 = i of 7= ^ of 10 = ^ of 13 -
C. J of 5 = J of 9 = J of 13 = 1 of 17 =
XVIII. DIVISION WITH REMAINDERS
Note. Have pupils state the nearest number of times the divisor is
contained in the dividend, ignoring the exact remainder. This will give
practice in finding trial divisors. Additional practice may be given with
similar examples put on the board.
A. 12)13 12)25 12)40 10)87 15)35 20)il
B. 25)60 21)43 14)30 11)40 11)78 13)43
C. 33)77 25)60 30)70 40)90 20)50 60)l30
XIX. DIVISION WITH REMAINDERS
A. 11)109 ll)l05 20)130 12)100 9)65
5. 27)50 11)100 32)50 45)80 23)37
a 28)60 26)49 52)90 58)l00 44)89
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GRADE IV. FOURTH SERIES 111
XX. PROBLEMS OF THE CARPENTER
1. A carpenter often uses a two-foot rule. It is some-
times divided into four parts, joined together by hinges.
When the carpenter folds this measure once there are
inches in each of the two parts.
2. When the carpenter folds his two-foot measure twice,
each of the four parts is inches long. (This may be
done in two ways.)
3. Nelson has a stick 15 inches long. He wants to cut
off pieces 4 inches long. How many such pieces can he
cut from his stick? (This can be done in two ways.
Which is the quicker way?)
4. Nelson has a stick 37 inches long. How can he use
it for a yardstick ? (This can be done in two ways.)
5. From a stick 1 inch wide and 11 inches long how
many pieces containing 2 square inches can be cut?
6. Mr. Harris, the carpenter, needs 6 screws for each of
8 pairs of hinges that he is putting on some doors. He
finds that he has 45 screws. Is that enough ? (You can
do this in three ways. Select the easiest way.)
7. Mr. Harris works 44 horns in a week. How many
full days of 8 hours each does he work ?
8. A package of screws contains a gross, but one screw
is lost from a package. How many sets of screws of
1 dozen in each set can be made up from this package ?
Addttionql Work. Hack pupil should write out and bring to class
a similar problem of his ounu
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112 PBACTICE EXERCISES IN MENTAL ARITHMETIC
XXI. FRACTIONAL PARTS WITH REMAINDERS
A i of $0.13= ^ of 10.15= ^ of $0.17= i of 19 in. =
A ^of22ft.= Jof25mi.= ^ofl4pt.= ^of28gal.=
C. ^of 13oz.= Jof251b.= Jof7da.= Jof29yr.=
XXII. DIVISION WITH REMAINDERS
A. 13j$27 14)$29 15)$35 19)$39 ISjIlO
B. $2lJ$40 $22)$50 $25)176 $30j$70 $40)|90
C. 12)40iZ 15)33i^ 20)451; 50)75 yd. 80)170 mi.
D. 8 oz.)25 oz. 11 lb.) 23 lb. 15 sec.) 33 sec. 14 cla.)26 da.
XXIIL DIVISION WITH REMAINDERS
A. 16)28 qt. 18)30 qt. 21)50 pt. 33)67 gi. 19)40 gal.
B. 22 qt.)41 qt. 33 gi.)65 gi. llgi.)75gi. 50pt.)99pt.
a 4)17 doz. 14)27 doz. 17)30 gr. 44)90 quires
2). 24 doz.) 55 doz. 39gr.)77gr. 44)90 quires
^. 60)500 sheets 60 sheets) 500 sheets
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GRADE IV. FOURTH SERIES 118
XXIV. PROBLEMS OF THE FARMER
1. Mr. Wilbur is a farmer living 13 miles from a
large dty. About ^ of the way to the city is the
nearest village, which is therefore about miles
from Mr. Wilbur's home.
2. If Mr. Wilbur's hens lay 50 eggs in one day he
has full dozen to sell.
3. If at another time Mt. Wilbur receives from a
peddler $1.50 for eggs that are selling for $0.60 a
dozen, he must have sold more than dozen.
4. In a large can Mr. Wilbur has 21 quarts of milk.
He pours it into two-quart bottles. He fills bottles
and has quart, or bottle left over.
5. If Mr. Wilbur chums 17 pounds of butter and
puts it into 5-pound boxes, he has boxes of butter.
6. In the month of June there are days. This
is weeks and days.
7. In Mr. Wilbur's bam the place where the cows
stand (the stanchions) is 43 feet long. If it is divided
up so that each cow has 4 feet of space in which to
stand, he can put cows in the stanchions.
8. Mr. Wilbur weighs out 19 pounds of com meal.
He makes it into a mash for his hens and chickens.
He has 4 pens of hens. To each pen he gives the
same amount of mash, and the rest he gives to his
chickens. Then he gives pounds to each pen of
hens and pounds to his chickens.
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114 PRACTICE EXERCISES IN MENTAL ARITHMETIC
XXV. PROBLEMS: MISCELLANEOUS
1. Mr. Sands drives an ice wagon. During July he
worked 26 days. How many days did he **take off"
in July?
2. One cake of ice weighs 25 pounds, but Mrs. Howe
wants only 15 pounds, so Mr. Sands must cut off
pounds.
3. Harry lives on a farm. One day he opens a new
2-bushel bag of com. How many quarts were in the
bag? (Do this in two ways-)
4. Harry pours ^ the bag of com into a box. How
many feedings will this be for the horse if he "gives
the horse 4 quarts at a time?
5. Sam buys 2 balls of twine, each containing 150 feet.
He ties the two balls together for a kite string. His string
is then feet long. (Do this in two ways.)
6. Three boys are playing ball in the school yard. The
ball accidentally breaks a window that costs $0.75 to re-
place. Each boy should pay . (Do this in two ways.)
7. Dick generally spends 25 minutes studying his
daily spelling lesson. If by studying hard he can
learn it in 15 minutes, how much time would he gain
in 6 days by studying hard?
8. The teacher has a box of 45 pencils. She asks 5
boys to sharpen them for her. If each boy takes the
same number, how many will he sharpen?
9. If 4 other boys help the 5 boys sharpen the 45
pencils, each will sharpen pencils.
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GRADE IV. FOURTH SERIES 115
XXVI. PROBLEMS: MISCELLANEOUS
1. In Sarah's school the children agree with the teacher
to spend 6 minutes a day in ** housekeeping" ; that is, in
helping keep the schoolroom neat and clean. How many
minutes does each pupil spend in this way during a school
week? This amounts to hours in a fortnight.
2. Mrs. Thomas buys a handkerchief for $0.35 and a
yard of ribbon for $0.22. She passes the clerk $0.75.
Count out her change.
3. A coal dealer buys coal from the mines for $9.10
a ton. He sells a ton to Mrs. Sampson for $11.25. How
much does the dealer make? Is this all profit?
4. Henry and James are measuring two di£Eerent strips
of wood. Henry says that his stick measures IJ feet.
James says his measures 18 inches. Which is longer, and
how much ? (Can you do this in two ways ?)
5. Harold earns money by doing odd jobs out of school.
A neighbor pays him at the rate of $0.15 an hour. If he
works only 30 minutes he should receive .
6. Harold works 20 minutes a day for 3 days. If
he receives $0.15 an horn*, how much should he receive
for his three days' work? (Do this in two ways.)
7. Mrs. Hart has 5 yards of cloth that she wishes to
make into aprons for 4 little girls. If she uses all the cloth
and makes all the aprons of the same size, how much cloth ;
will be used for each apron ? (Do this in two ways.)
AdditUmal Work. Each pupil should write out and bring to class
a similar problem of his own.
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